Lattice Hamiltonian automatic generator and lattice Hamiltonian automatic generation method

Abstract

The present application discloses a lattice Hamiltonian automatic generator and a lattice Hamiltonian automatic generation method. The lattice Hamiltonian automatic generator includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module. The lattice basis vector definition module is configured to perform programmatic analysis on the input basis vector parameters to generate primitive cells and lattice structure data. The lattice point filling module is configured to perform lattice point filling on the primitive cells according to the lattice structure data and determine the lattice point filling result. The Hamiltonian generation module is configured to automatically generate a lattice Hamiltonian based on the lattice structure data and the lattice point filling result. In this way, the lattice Hamiltonian automatic generator provided in the embodiment of the present application automates and modularizes the process of generating the lattice Hamiltonian, thereby avoiding the problem of excessive manual intervention in the traditional lattice Hamiltonian construction process, thereby improving the efficiency and accuracy of the lattice Hamiltonian construction.

Description

Technical Field

[0001] The present application relates to the field of quantum simulation computing, and more specifically, to a lattice Hamiltonian automatic generator and a lattice Hamiltonian automatic generation method. Background Art

[0002] The lattice Hamiltonian is fundamental to condensed matter physics research. Its construction is essentially a mathematical abstraction of real physical systems. However, in related technologies, the process of constructing the lattice Hamiltonian involves excessive user involvement and is highly dependent on manual labor, resulting in high error rates in the construction of the lattice Hamiltonian. Summary of the Invention

[0003] The present application provides a lattice Hamiltonian automatic generator.

[0004] The embodiment of the present application provides a lattice Hamiltonian automatic generator, which includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module;

[0005] The lattice basis vector definition module is configured to perform programmatic analysis on input basis vector parameters to generate primitive cells and lattice structure data;

[0006] The lattice filling module is configured to perform lattice filling on the unit cell according to the lattice structure data and determine a lattice filling result;

[0007] The Hamiltonian generation module is configured to automatically generate the lattice Hamiltonian according to the lattice structure data and the lattice filling result.

[0008] Thus, the lattice Hamiltonian automatic generator provided in the embodiment of the present application includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module. Among them, the lattice basis vector definition module can perform programmatic analysis on the input basis vector parameters to generate primitive cells and lattice structure data. The lattice point filling module can perform lattice point filling on the primitive cells according to the lattice structure data and determine the lattice point filling result. The Hamiltonian generation module can automatically generate the lattice Hamiltonian based on the lattice structure data and the lattice point filling result. In this way, the lattice Hamiltonian automatic generator provided in the embodiment of the present application avoids the problem of much manual intervention in the traditional lattice Hamiltonian construction process by automating and modularizing the process of generating the lattice Hamiltonian, thereby improving the efficiency and accuracy of the lattice Hamiltonian construction.

[0009] In some embodiments, the basis vector parameters include the cell body dimensions of the primitive cell, a list of primitive cell basis vectors, a list of lattice coordinates, a lattice type, a list of lattice vectors, a lattice size flag, a lattice length, and / or a boundary condition type, and the lattice basis vector definition module is configured to:

[0010] Determine the primitive cell according to the cell body dimension, the primitive cell basis vector list and the grid point coordinate list;

[0011] determining lattice configuration data according to the lattice type and the lattice vector list;

[0012] determining lattice physical property data according to the lattice size flag, the lattice length and / or the boundary condition type;

[0013] The lattice structure data is determined according to the unit cell, the lattice configuration data and the lattice physical property data.

[0014] In this way, the lattice basis vector definition module can determine the primitive cell according to the cell body dimensions, the primitive cell basis vector list and the lattice coordinate list. Next, the lattice basis vector definition module can determine the lattice configuration data according to the lattice type and the lattice vector list. Then, the lattice basis vector definition module can determine the lattice physical property data according to the lattice size mark, lattice length and / or boundary condition type. Finally, the lattice basis vector definition module can determine the lattice structure data according to the primitive cell, lattice configuration data and lattice physical property data. In this way, by automatically parsing the basis vector parameters input by the user, the primitive cell and lattice structure data are generated, avoiding the tedious process of manually drawing the lattice, significantly improving the efficiency of lattice model construction, and avoiding the geometric errors when manually marking the lattice coordinates or basis vectors, ensuring the accuracy of the lattice model.

[0015] In some embodiments, the lattice basis vector definition module is configured to:

[0016] In response to a lattice configuration selection operation, the lattice configuration data is determined from a preset lattice configuration template, wherein the preset lattice configuration template includes a chain lattice, a square lattice, a triangle lattice, a honeycomb lattice, and a cage lattice.

[0017] The lattice basis definition module can also respond to lattice configuration selection operations and determine lattice configuration data from preset lattice configuration templates, including chain lattices, square lattices, triangular lattices, honeycomb lattices, and cage lattices. This allows lattice configuration data to be generated directly from preset lattice configuration templates through lattice configuration selection, eliminating the need to manually enter basis parameters or geometric rules, significantly reducing lattice construction time.

[0018] In some embodiments, the grid filling result includes grid filling information and supercell definition information, and the grid filling module is configured to:

[0019] Determining initial lattice filling information according to the input atom type and spin state, the lattice type, the primitive cell basis vector list, and the lattice coordinate list;

[0020] The grid point filling information is determined according to the initial grid point filling information.

[0021] The resulting lattice filling result includes both lattice filling information and supercell definition information. The lattice filling module determines the initial lattice filling information based on the input atom types and spin states, as well as the lattice type, the list of unit cell basis vectors, and the list of lattice coordinates. The lattice filling module then determines the lattice filling information based on the initial lattice filling information. This standardized process reduces manual steps, avoids operational errors and information omissions caused by manual filling, and improves the efficiency of lattice Hamiltonian generation.

[0022] In some embodiments, the grid filling module is configured to:

[0023] In the case where a defect needs to be constructed for the primitive cell, determining the grid point filling information according to the initial grid point filling information, the input defect primitive cell coordinate list and the defect type;

[0024] Without constructing defects in the primitive cells, the initial grid point filling information is determined as the grid point filling information.

[0025] In this way, the grid filling module can determine the grid filling information based on the initial grid filling information, the input defect cell coordinate list, and the defect type, even when defects need to be constructed in the primitive cell. The grid filling module can then determine the initial grid filling information as the grid filling information without constructing defects in the primitive cell. This allows precise modification of specific primitive cells using the defect cell coordinate list and defect type.

[0026] In some embodiments, the grid filling result includes supercell definition information, and the grid filling module is configured to:

[0027] The supercell definition information is determined according to the lattice type and the input supercell lattice vector, wherein the supercell lattice vector is represented by the primitive cell basis vector list.

[0028] The lattice filling module now determines the supercell definition information based on the lattice type and the input supercell lattice vectors, which are represented as a list of primitive cell basis vectors. This standardized process reduces manual steps, avoids operational errors and information omissions caused by manual filling, and improves the efficiency of lattice Hamiltonian generation.

[0029] In some embodiments, the lattice structure data includes a list of primitive cell basis vectors, the lattice filling result includes supercell lattice vectors, and the Hamiltonian generation module is configured to:

[0030] Determining a zero matrix according to the grid filling result and the input Hamiltonian type;

[0031] Determining transition matrix elements according to the zero matrix, the primitive cell basis vector list, the supercell lattice vector and input transition parameters;

[0032] determining interaction matrix elements according to the grid filling result and the input interaction parameters;

[0033] The lattice Hamiltonian is determined based on the transition matrix element and the interaction matrix element.

[0034] In this way, the lattice structure data includes a list of primitive cell basis vectors, and the lattice filling results include supercell lattice vectors. The Hamiltonian generation module can determine the zero matrix based on the lattice filling results and the input Hamiltonian type. Next, the Hamiltonian generation module can determine the transition matrix elements based on the zero matrix, the primitive cell basis vector list, the supercell lattice vectors, and the input transition parameters. Then, the Hamiltonian generation module can determine the interaction matrix elements based on the lattice filling results and the input interaction parameters. Finally, the Hamiltonian generation module can determine the lattice Hamiltonian based on the transition matrix elements and the interaction matrix elements. In this way, the Hamiltonian generation module can realize the full-process procedural generation from lattice geometry to lattice Hamiltonian, without the need for manual intervention in matrix construction details, thereby improving the efficiency of lattice Hamiltonian generation.

[0035] In some embodiments, the lattice structure data includes lattice symmetry parameters, and the Hamiltonian generation module is configured to:

[0036] An optimized lattice Hamiltonian is determined according to the lattice symmetry parameters and the lattice Hamiltonian.

[0037] In this way, the lattice structure data includes lattice symmetry parameters, and the Hamiltonian generation module can determine the optimized lattice Hamiltonian based on the lattice symmetry parameters and the lattice Hamiltonian. In this way, the lattice symmetry parameters can be used to identify redundant elements in the Hamiltonian matrix, thereby reducing the matrix dimension and computational complexity.

[0038] In some embodiments, the lattice Hamiltonian automatic generator further includes a quantum cluster method interface module, and the quantum cluster method interface module is configured to:

[0039] Based on a preset quantum cluster method, formatted Hamiltonian data is determined according to the lattice Hamiltonian.

[0040] Thus, the lattice Hamiltonian automatic generator also includes a quantum cluster method interface module, which determines the formatted Hamiltonian data based on the lattice Hamiltonian, based on a pre-set quantum cluster method. This module converts the automatically generated lattice Hamiltonian into the formatted data required by the pre-set quantum cluster method, ensuring that the Hamiltonian data can be directly input into subsequent calculation processes, reducing the tedious manual format conversion process.

[0041] In certain embodiments, during the automatic generation of the lattice Hamiltonian, the basis vector parameters, the atom type, the spin state, the supercell lattice vector and / or the Hamiltonian type can be adjusted.

[0042] In this way, during the automatic generation of the lattice Hamiltonian, the basis vector parameters, atom types, spin states, supercell lattice vectors, and / or Hamiltonian type can be adjusted. This allows for the adaptation of lattice models from simple to complex through multi-parameter adjustment, meeting diverse needs.

[0043] An embodiment of the present application provides a method for automatically generating a lattice Hamiltonian. The method is based on the above-mentioned lattice Hamiltonian automatic generator, and the method includes:

[0044] Based on the lattice basis vector definition module, the input basis vector parameters are programmatically parsed to generate primitive cell and lattice structure data;

[0045] Based on the lattice filling module, lattice filling is performed on the unit cell according to the lattice structure data to determine a lattice filling result;

[0046] Based on the Hamiltonian generation module, the lattice Hamiltonian is automatically generated according to the lattice structure data and the lattice filling result.

[0047] In this way, the lattice basis vector definition module programmatically analyzes the input basis vector parameters to generate the primitive cell and lattice structure data. Next, the lattice point filling module performs lattice filling on the primitive cell based on the lattice structure data, and the lattice filling result is determined. Finally, the Hamiltonian generation module automatically generates the lattice Hamiltonian based on the lattice structure data and the lattice point filling result. By automating and modularizing the lattice Hamiltonian generation process, the traditional manual intervention problem of lattice Hamiltonian construction is avoided, thereby improving the efficiency and accuracy of lattice Hamiltonian construction.

[0048] Additional aspects and advantages of the embodiments of the present application will be given in part in the description below, and in part will become obvious from the description below, or will be learned through practice of the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0050] Figure 1 This is one of the structural diagrams of the lattice Hamiltonian automatic generator according to the embodiment of the present application;

[0051] Figure 2 is a schematic diagram of a supercell configuration according to an embodiment of the present application;

[0052] Figure 3 This is the second flow chart of the lattice Hamiltonian automatic generator according to the embodiment of the present application;

[0053] Figure 4 Schematic diagram of the lattice Hamiltonian construction process according to the embodiment of the present application;

[0054] Figure 5 It is a flow chart of the method for automatically generating the lattice Hamiltonian according to the embodiment of the present application. DETAILED DESCRIPTION

[0055] The embodiments of the present application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the embodiments of the present application, and should not be understood as limiting the embodiments of the present application.

[0056] The lattice Hamiltonian plays a cornerstone role in the research fields of condensed matter physics and materials science. It is a key tool for mathematically abstracting and modeling real physical systems. Through precise mathematical language, it extracts complex physical phenomena such as the interactions between electrons and atomic nuclei in crystal structures and the strong correlations between electrons into computable lattice Hamiltonian expressions, providing a theoretical foundation for in-depth exploration of key physical properties such as the electronic structure, phase transition behavior, and transport properties of materials.

[0057] However, in related technologies, the construction process of the lattice Hamiltonian faces significant challenges. Specifically, from the definition of the lattice configuration, the selection of the superlattice basis vectors, to the setting of the lattice filling rules and the filling of the lattice Hamiltonian, each key link is highly dependent on manual operation. In practical applications, researchers need to manually define the basis vector parameters of the superlattice and fill in the lattice information one by one according to different lattice types (such as chain lattices, square lattices, and honeycomb lattices, etc.) and computational requirements, and clarify whether each lattice point is filled with atoms, atomic types (bosons or fermions), and spin states, so as to construct the lattice Hamiltonian.

[0058] Thus, this strong dependence on manual labor brings about many problems. First, manual operation is inevitably subjective and arbitrary. Different researchers may adopt different unit cell selection methods or superlattice partitioning strategies for the same physical system, and different choices will directly lead to differences in the Hamiltonian construction rules, and then introduce human errors, resulting in a high error rate in the lattice Hamiltonian construction. For example, when dealing with a two-dimensional square lattice, if the selection of the superlattice basis vector is changed from the default (1, 0), (0, 1) to ( , )、( ,- ), the form of the lattice Hamiltonian will change, resulting in deviations in the calculation results.

[0059] Furthermore, when parameters such as the lattice configuration, many-body model, or superlattice size change, the entire lattice Hamiltonian construction process needs to be restarted and fully adjusted. For example, when switching from studying a simple spinless fermion system to a spin system, or expanding from a two-dimensional lattice to a three-dimensional lattice, researchers must redefine the lattice basis vectors, lattice point filling rules, and manually modify the lattice Hamiltonian. This repetitive work not only consumes a lot of manpower and time, but also easily leads to omissions due to the cumbersome process, further increasing the risk of errors.

[0060] Furthermore, manually constructing the Hamiltonian is inefficient in large-scale numerical simulations. As the dimensionality of the computational system increases, the complexity of strongly correlated electronic systems grows exponentially, placing extremely high demands on computing resources and modeling efficiency. Traditional manual operation methods are unable to adapt to this demand, potentially delaying research progress and invalidating the entire simulation results due to the inability to promptly correct manual errors.

[0061] Based on the above questions, please refer to Figure 1 An embodiment of the present application provides a lattice Hamiltonian automatic generator 100 , which includes a lattice basis vector definition module 10 , a lattice point filling module 20 and a Hamiltonian generation module 30 .

[0062] The lattice basis vector definition module 10 is configured to perform programmatic analysis on the input basis vector parameters to generate primitive cells and lattice structure data.

[0063] The lattice filling module 20 is configured to perform lattice filling on the primitive cells according to the lattice structure data and determine the lattice filling result.

[0064] The Hamiltonian generation module 30 is configured to automatically generate a lattice Hamiltonian according to the lattice structure data and the lattice filling result.

[0065] Specifically, the essence of the lattice Hamiltonian automatic generator 100 is to decompose the lattice Hamiltonian construction process into three logically independent and interconnected modules through modular programming, namely the lattice basis vector definition module 10, the lattice point filling module 20 and the Hamiltonian generation module 30, replacing traditional manual operations in a programmed manner, realizing full process automation from lattice geometry definition to Hamiltonian generation, and replacing the tedious process of traditional manual construction of Hamiltonian.

[0066] The lattice basis vector definition module 10 is the foundation. The lattice structure data (such as unit cells and lattice structure data) generated by this module provides geometric input for subsequent modules. The lattice point filling module 20 further refines the physical properties of the lattice points (such as spin type) based on the lattice structure and outputs the lattice point filling results. The Hamiltonian generation module 30, as the core, integrates the data from the lattice basis vector definition module 10 and the lattice point filling module 20 to automatically generate the lattice Hamiltonian, achieving the mapping from structure to physical model.

[0067] The lattice Hamiltonian refers to a matrix that describes the interactions and energy of particles in a lattice system and is automatically constructed by the Hamiltonian generation module 30 .

[0068] Programmatic analysis involves using pre-programmed algorithms to mathematically analyze and structure the user-entered basis vector parameters, automatically generating computer-readable geometric structure data. For example, if the primitive cell basis vectors are (1, 0) and (0, 1), the program can automatically generate the lattice coordinate network of a two-dimensional square lattice.

[0069] A unit cell is the smallest repeating unit of a crystal structure, capable of completely filling the entire crystal through translation. While the unit cell is not unique, it has a uniform volume. A unit cell can be thought of as the "building block" of a crystal. For example, a unit cell of graphene contains two carbon atoms, while a unit cell of a simple cubic lattice contains only one lattice point. The definition of the unit cell directly determines the periodicity and symmetry of the lattice.

[0070] Lattice structure data refers to the complete lattice geometry generated by translating unit cells through basis vectors. This includes the lattice type, lattice dimensions, lattice basis vectors, lattice size, and boundary conditions. Lattice structure data is a digital representation of a crystal. For example, the structure data of a two-dimensional square lattice can be described as "an infinite grid generated by translating unit cells (1, 0) and (0, 1), with open boundary conditions."

[0071] The lattice filling result refers to the result of configuring the physical properties of the lattice points in the primitive cell based on the lattice structure data, including lattice filling information and supercell definition information.

[0072] In summary, the lattice Hamiltonian automatic generator provided in the embodiment of the present application includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module. Among them, the lattice basis vector definition module can perform programmatic analysis on the input basis vector parameters to generate primitive cells and lattice structure data. The lattice point filling module can perform lattice point filling on the primitive cells according to the lattice structure data and determine the lattice point filling result. The Hamiltonian generation module can automatically generate the lattice Hamiltonian based on the lattice structure data and the lattice point filling result. In this way, the lattice Hamiltonian automatic generator 100 provided in the embodiment of the present application avoids the problem of much manual intervention in the traditional lattice Hamiltonian construction process by automating and modularizing the process of generating the lattice Hamiltonian, thereby improving the efficiency and accuracy of the lattice Hamiltonian construction.

[0073] In some embodiments, the basis vector parameters include the cell body dimensions of the primitive cell, a list of primitive cell basis vectors, a list of lattice coordinates, a lattice type, a list of lattice vectors, a lattice size flag, a lattice length, and / or a boundary condition type. The lattice basis vector definition module 10 is configured to:

[0074] Determine the primitive cell based on the cell body dimensions, primitive cell basis vector list, and grid point coordinate list;

[0075] Determine lattice configuration data based on lattice type and lattice vector list;

[0076] determining lattice physical property data according to a lattice size flag, a lattice length and / or a boundary condition type;

[0077] The lattice structure data is determined based on the unit cell, lattice configuration data and lattice physical property data.

[0078] Specifically, the basis vector parameters include the cell body dimensions of the primitive cell, a list of primitive cell basis vectors, a list of lattice coordinates, a lattice type, a list of lattice vectors, a lattice size flag, a lattice length and / or a boundary condition type.

[0079] Among them, the cell body dimension, the primitive cell basis vector list and the grid coordinate list are all related parameters of the primitive cell.

[0080] The cell body dimension of a primitive cell refers to the spatial dimension of the primitive cell, such as one-dimensional, two-dimensional or three-dimensional, which can determine the geometric spatial properties of the primitive cell. For example, a two-dimensional primitive cell has two basis vectors, and a three-dimensional primitive cell has three basis vectors.

[0081] The primitive cell basis vector list refers to the basis vector coordinates of each dimension of the primitive cell, which is used to describe the shape and size of the primitive cell. For example, the basis vectors of a two-dimensional primitive cell can be (1, 0) and (0, 1) (square primitive cell), or (1, 0) and ( , The list of basis vectors directly determines the volume and symmetry of the cell.

[0082] The grid coordinate list refers to the coordinate value of each grid point in the primitive cell (relative to the coordinate system of the primitive cell basis vector), which can determine the distribution of particles in the primitive cell and is the geometric basis for subsequent grid filling (such as defining atomic type and spin).

[0083] The lattice type, lattice vector list, lattice size flag, lattice length and boundary condition type are lattice related parameters.

[0084] The lattice type refers to the geometric type of the lattice, such as chain lattice, square lattice, triangular lattice, honeycomb lattice, and cage lattice. It should be noted that lattice types are usually associated with default lattice basis vectors, but users can also break through these restrictions by defining custom basis vectors.

[0085] The lattice vector list refers to the expansion vectors of each dimension of the lattice. It is used to describe how the unit cell is translated to form a complete lattice. It can determine the spatial expansion direction of the lattice. Its length and direction can be the same as or different from the unit cell basis vector.

[0086] The lattice size flag is a parameter used to identify whether the lattice is finite or infinite. If the lattice is finite, you must specify the lattice length. If the lattice is infinite, you do not need to enter a length.

[0087] Lattice length refers to the number of lattice points or the physical length in each dimension.

[0088] The boundary condition type refers to how the lattice is treated at its spatial boundaries. These conditions include periodic boundary conditions (where the lattice is connected end to end) and open boundary conditions (where the lattice is truncated at its edges). Boundary conditions affect the computation of transition terms across boundaries in the Hamiltonian. For example, periodic boundaries introduce a phase factor, while open boundaries ignore interactions beyond the boundary.

[0089] First, a primitive cell is constructed based on the user-entered cell dimensions, a list of primitive cell basis vectors, and a list of grid point coordinates. The specific operations are: 1. The spatial dimensions of the primitive cell are determined based on the cell dimensions (e.g., a 2D primitive cell requires two basis vectors); 2. The geometric framework of the primitive cell is constructed using the primitive cell basis vector list; 3. The grid point coordinate list is used to assign specific locations to each grid point within the primitive cell.

[0090] Next, when the user selects a custom lattice, the lattice configuration data is determined based on the lattice type and lattice vector list input by the user.

[0091] Then, the lattice physical property data is determined based on the lattice size flag, lattice length and boundary condition type input by the user.

[0092] Finally, the primitive cell definition, lattice configuration data, and physical property data are merged to form a complete lattice structure description (i.e., lattice structure data) for use by the subsequent lattice filling module 20 and Hamiltonian generation module 30.

[0093] In this way, the lattice basis vector definition module can determine the primitive cell according to the cell body dimensions, the primitive cell basis vector list and the lattice coordinate list. Next, the lattice basis vector definition module can determine the lattice configuration data according to the lattice type and the lattice vector list. Then, the lattice basis vector definition module can determine the lattice physical property data according to the lattice size mark, lattice length and / or boundary condition type. Finally, the lattice basis vector definition module can determine the lattice structure data according to the primitive cell, lattice configuration data and lattice physical property data. In this way, by automatically parsing the basis vector parameters input by the user, the primitive cell and lattice structure data are generated, avoiding the tedious process of manually drawing the lattice, significantly improving the efficiency of lattice model construction, and avoiding the geometric errors when manually marking the lattice coordinates or basis vectors, ensuring the accuracy of the lattice model.

[0094] In some embodiments, the lattice basis vector definition module 10 is configured to:

[0095] In response to the lattice configuration selection operation, lattice configuration data is determined from a preset lattice configuration template.

[0096] Specifically, the lattice configuration selection operation refers to the behavior of the user selecting the type of lattice through the interface or parameter input.

[0097] The lattice basis vector definition module 10 may provide a preset lattice for the user to select. The user may select to use the preset lattice (rather than a custom lattice) through the module interface, for example, selecting a “square lattice” in a two-dimensional scene.

[0098] Next, the system retrieves the predefined parameters for the corresponding lattice from a built-in library of preset lattice configuration templates based on the user's selection. For example, for a square lattice, the default basis vectors are the two-dimensional orthogonal vectors (1, 0) and (0, 1), and the lattice points are arranged in a square.

[0099] Subsequently, the system automatically generates the geometric structure data of the lattice based on the template parameters.

[0100] The lattice basis definition module can also respond to lattice configuration selection operations and determine lattice configuration data from preset lattice configuration templates, including chain lattices, square lattices, triangular lattices, honeycomb lattices, and cage lattices. This allows lattice configuration data to be generated directly from preset lattice configuration templates through lattice configuration selection, eliminating the need to manually enter basis parameters or geometric rules, significantly reducing modeling time.

[0101] In some embodiments, the grid filling result includes grid filling information and supercell definition information, and the grid filling module 20 is configured to:

[0102] Determine the initial grid filling information based on the input atom type and spin state, lattice type, primitive cell basis vector list and lattice coordinate list;

[0103] Determine the grid filling information based on the initial grid filling information.

[0104] Specifically, the atomic type refers to the type of particles that populate the lattice points, including bosons and fermions. Bosons are particles that follow Bose-Einstein statistics (such as photons and phonons), and their Hamiltonian transition terms do not involve spin exchange symmetry. Fermions are particles that follow Fermi-Dirac statistics (such as electrons and protons), and the Pauli exclusion principle must be considered. The Hamiltonian may contain spin-dependent terms (such as spin-orbit coupling and exchange interaction).

[0105] The spin state describes the spin properties of a particle, including both spin-free and spin-on states. For spin-free states, the spin degree of freedom is ignored (e.g., electrons in a simplified model), and the lattice Hamiltonian dimension is related only to the number of orbitals. For spin-on states, spin degrees of freedom are present (e.g., electron spin up / down), and the Hamiltonian requires the inclusion of a spin index.

[0106] The initial grid filling information refers to the default grid filling rules that are automatically generated based on the lattice type, the list of unit cell basis vectors, the list of grid coordinates, and the atom types and spin states entered by the user.

[0107] The resulting lattice filling result includes both lattice filling information and supercell definition information. The lattice filling module determines the initial lattice filling information based on the input atom types and spin states, as well as the lattice type, the list of unit cell basis vectors, and the list of lattice coordinates. The lattice filling module then determines the lattice filling information based on the initial lattice filling information. This standardized process reduces manual steps, avoids operational errors and information omissions caused by manual filling, and improves the efficiency of lattice Hamiltonian generation.

[0108] In some embodiments, the grid filling module 20 is configured to:

[0109] When defects need to be constructed for primitive cells, the grid filling information is determined based on the initial grid filling information, the input defect primitive cell coordinate list and the defect type;

[0110] Without constructing defects in the primitive cells, the initial grid filling information is determined as the grid filling information.

[0111] Specifically, constructing defects in a primitive cell refers to modifying the grid filling rules of a specific primitive cell to a non-default state during the grid filling process, thereby breaking the consistency of the primitive cell grid filling. Under normal circumstances, the grid filling module 20 defaults to the same grid filling rules for all primitive cells (such as full filling, the same atomic type and spin). If defects are required, the user is allowed to individually adjust the filling rules of a specific primitive cell, such as changing whether a grid point in the primitive cell is filled with atoms, the type of atoms filled with atoms, or the spin state, thereby simulating defects in the crystal structure.

[0112] The defective primitive cell coordinate list is a user-entered set of primitive cell coordinates for which defects need to be constructed. This list is used to locate the primitive cells whose filling rules need to be modified. Generally speaking, each primitive cell has unique coordinates in the lattice (such as (x, y) coordinates in a two-dimensional lattice or (x, y, z) coordinates in a three-dimensional lattice). Users specify which primitive cells require defect modification by entering a specific coordinate list (such as primitive cell coordinates (1, 1) and (2, 3)).

[0113] The defect type refers to the specific modification made to the grid packing rules of the target primitive cell, including the grid packing state, atomic species, and atomic spin. The defect type is a specific instruction for modifying the grid packing rules of the primitive cell and must be used in conjunction with the defect cell coordinates.

[0114] In this way, the grid filling module can determine the grid filling information based on the initial grid filling information, the input defect cell coordinate list, and the defect type, even when defects need to be constructed in the primitive cell. The grid filling module can then determine the initial grid filling information as the grid filling information without constructing defects in the primitive cell. This allows precise modification of specific primitive cells using the defect cell coordinate list and defect type.

[0115] In some embodiments, the grid filling result includes supercell definition information, and the grid filling module 20 is configured to:

[0116] Determine the supercell definition information based on the lattice type and the input supercell lattice vector.

[0117] Specifically, the supercell lattice vector refers to the vector used to describe the geometric structure of the supercell. It is expressed based on the unit cell basis vector (the dimension vector of the unit cell) and reflects the size and shape of the supercell in the lattice. For example, if the lattice dimension is two-dimensional, the user enters two supercell lattice vector coordinates. The value of the supercell lattice vector can determine the size and shape of the supercell. For example, the vectors (1, 0) and (0, 1) indicate that the supercell is expanded by 1 times in the direction of the unit cell basis vector and contains 1 unit cell. In addition, the definition of the supercell lattice vector directly affects the simulation of long-range correlation effects in the quantum cluster method. For example, by dividing the supercell by different vectors, the electron correlation behavior at different scales can be studied.

[0118] Supercell definition information refers to the complete information describing the supercell structure, which is determined by the supercell lattice vector and related parameters. Its core is to clarify the geometric configuration of the supercell, the number of primitive cells included, and the arrangement, providing structured input for the subsequent Hamiltonian generation. Supercell definition information is the basic data of the Hamiltonian generation module 30, which is used to distinguish between local transition terms within the supercell and cross-boundary transition terms. For example, when the target primitive cell of the transition term is inside the supercell, it is retained as a local term; if it exceeds the boundary, it is decomposed by the supercell lattice vector, mapped to the equivalent position of the adjacent supercell, and the momentum space phase factor is calculated.

[0119] Furthermore, supercells are the fundamental unit of quantum cluster methods for processing strongly correlated systems, and their definition directly impacts the computational accuracy of quantum cluster methods. For example, the lattice Hamiltonian generated by different supercell lattice vectors must be passed to subsequent quantum cluster methods for energy spectrum analysis.

[0120] See also Figure 2 , Figure 2 Schematic diagram of supercell configuration obtained from different supercell definition information. Figure 2 The vectors of the supercell configuration on the left are (1, 0), (0, 1), Figure 2 The vector of the supercell configuration on the left is ( , ), ( ,- ).

[0121] The lattice filling module now determines the supercell definition information based on the lattice type and the input supercell lattice vectors, which are represented as a list of primitive cell basis vectors. This standardized process reduces manual steps, avoids operational errors and information omissions caused by manual filling, and improves the efficiency of lattice Hamiltonian generation.

[0122] The lattice structure data includes a list of primitive cell basis vectors, the lattice filling result includes supercell lattice vectors, and the Hamiltonian generation module 30 is configured as follows:

[0123] Determine the zero matrix based on the grid filling result and the input Hamiltonian type;

[0124] Determine the transition matrix elements based on the zero matrix, the primitive cell basis vector list, the supercell lattice vectors and the input transition parameters;

[0125] Determine the interaction matrix elements based on the grid filling results and the input interaction parameters;

[0126] The lattice Hamiltonian is determined based on the transition matrix elements and the interaction matrix elements.

[0127] Specifically, the Hamiltonian type refers to the Hamiltonian category used to distinguish different physical models, such as the Hubbard model and the Heisenberg model. Different models correspond to different Hamiltonian expressions and physical meanings. For example, the Hubbard model primarily describes electron hopping and Coulomb interactions and is applicable to strongly correlated electron systems; the Heisenberg model focuses on spin interactions and is used to study magnetic systems. The user must enter the Hamiltonian type to determine the basic form of matrix construction. The lattice Hamiltonian automatic generator 100 then invokes the corresponding calculation rules based on the type.

[0128] The zero matrix is ​​a matrix initialized to all zeros and serves as the basic framework for constructing the lattice Hamiltonian. Its dimension is determined by the number of orbitals in the supercell (each supercell contains N×S orbitals, where N is the number of orbitals in the unit cell and S is the number of supercell points). For example, if the supercell has four points, with one orbital per point (no spin), the zero matrix dimension is 4×4; if spin is considered, with two orbitals per point (spin up / spin down), the dimension is 8×8.

[0129] Transition parameters are physical quantities that describe the transition of electrons (or particles) between different lattice points (or orbitals), typically expressed as complex transition strengths. Transition parameters reflect the ability of particles to move within a lattice, such as the tunneling strength t in the Hubbard model. Transition parameters are determined by combining a list of unit cell basis vectors with the supercell lattice vectors to determine the lattice point pairs where the transition occurs and the corresponding displacement vectors.

[0130] Transition matrix elements refer to the matrix elements calculated based on transition parameters, primitive cell basis vectors and supercell lattice vectors, which describe the transition contributions between different orbitals.

[0131] Interaction parameters are physical quantities that describe the interactions between particles, such as the Coulomb repulsion energy U in the Hubbard model. It should be noted that interaction parameters are typically local terms, acting only on orbitals within the same lattice point (or unit cell). Furthermore, interaction parameters must be combined with the lattice filling (e.g., atom type and spin state) to determine the type and strength of the interaction. For example, electrons with opposite spins interact with each other at the same lattice point.

[0132] The interaction matrix element refers to the matrix element calculated based on the interaction parameters and grid filling results, which describes the interaction contribution between particles in the same grid point (or unit cell).

[0133] The lattice Hamiltonian refers to the complete matrix obtained by integrating the transition matrix elements and the interaction matrix elements. It describes the energy state of the entire supercell system and is the core input for quantum cluster method calculations.

[0134] First, based on the lattice filling result (the number of lattice points S determined by the supercell lattice vector) and the Hamiltonian type (determining the number of orbitals N), a zero matrix with dimensions N × S × N × S is generated as a blank frame.

[0135] Next, the input transition parameters are analyzed to determine the scope of each transition term (within the supercell or across the boundary). If it is a cross-boundary transition, the displacement vector is decomposed by the primitive cell basis vector , calculate the phase factor. Finally, integrate all transition terms and fill the off-diagonal elements of the zero matrix to obtain the transition matrix.

[0136] Then, based on the grid filling situation (such as whether atoms are filled and the spin direction), the interaction points are determined (such as electrons with opposite spins at the same grid point), and the interaction parameters are converted into matrix diagonal elements.

[0137] Finally, the transition matrix elements and the interaction matrix elements are superimposed into the zero matrix to obtain the final lattice Hamiltonian.

[0138] For example, if the Hamiltonian type is the Hubbard model, the Hubbard model Hamiltonian can be written as follows:

[0139] in, is the particle generation operator at grid point i, is the particle annihilation operator at lattice point i, which is used to describe the quantum state operation of fermions (such as electrons); is the transition integral between lattice points i and j (i.e., transition parameter), which characterizes the tunneling ability of electrons between different lattice points; is the four-body interaction coefficient, which describes the multi-body interaction (such as Coulomb interaction) between lattice points i, j, k, and l, and is usually used to characterize the nonlocal effect of electron-electron interaction; is the particle generation operator at grid point j, is the particle annihilation operator at the lattice point k, is the particle annihilation operator at the lattice point l.

[0140] Assume that there are N orbitals in the primitive cell and S lattice points in each supercell, then there are N×S orbitals in each supercell.

[0141] First, the transition terms between primitive cells are mapped to supercells: 1. Traverse all transition parameters in the primitive cell Hamiltonian (such as The transition coefficient , where R represents the displacement vector between different supercells, characterizing the relative position offset of the unit cell in the lattice). 2. For each transition parameter , determine its scope of action: if the target unit cell is inside the supercell, it is retained as a local term within the supercell; if the target unit cell exceeds the supercell, the transition is mapped to the equivalent position of the adjacent supercell through superlattice vector decomposition, and the corresponding supercell displacement vector Δ is recorded.

[0142] Next, the momentum-space phase factor is calculated: for each non-zero supercell displacement Δ (i.e., when the transition term crosses the supercell boundary), the real-space displacement vector is calculated: ,in, is the supercell displacement vector, which represents the spatial displacement when the transition term crosses the supercell boundary, and is represented by the primitive cell basis vector Linear combination; is the displacement vector In the primitive cell base vector Components in the directions (i=1,2,3 correspond to the three dimensions of the three-dimensional lattice); is the basis vector of the primitive cell, which is used to define the geometric structure of the lattice. Solve for the phase factor of momentum q , where q is the wave vector in momentum space, representing the momentum state of the electron; the phase factor Used to describe the phase shift caused by the wave vector q when electrons cross the supercell boundary.

[0143] Finally, the transition matrix is ​​integrated to obtain T(q): 1. For each supercell displacement Δ, extract its corresponding transition matrix t( ) (dimension is N×N, each element corresponds to the transition coefficient between the primitive cell orbitals). 2. Weighted sum of the contributions of all non-zero displacements: ,in, is a transition matrix of dimension N×N, where N is the number of orbitals in the primitive cell and the matrix elements correspond to the transition coefficients between the primitive cell orbitals; T(q) is an effective transition matrix of dimension N×S×N×S, where S is the number of lattice points in the supercell, describing the effective transitions of all orbitals in the supercell under momentum q.

[0144] In this way, the lattice structure data includes a list of primitive cell basis vectors, and the lattice filling results include supercell lattice vectors. The Hamiltonian generation module can determine the zero matrix based on the lattice filling results and the input Hamiltonian type. Next, the Hamiltonian generation module can determine the transition matrix elements based on the zero matrix, the primitive cell basis vector list, the supercell lattice vectors, and the input transition parameters. Then, the Hamiltonian generation module can determine the interaction matrix elements based on the lattice filling results and the input interaction parameters. Finally, the Hamiltonian generation module can determine the lattice Hamiltonian based on the transition matrix elements and the interaction matrix elements. In this way, the Hamiltonian generation module can realize the full-process procedural generation from lattice geometry to lattice Hamiltonian, without the need for manual intervention in matrix construction details, thereby improving the efficiency of lattice Hamiltonian generation.

[0145] In some embodiments, the lattice structure data includes lattice symmetry parameters, and the Hamiltonian generation module 30 is configured to:

[0146] According to the lattice symmetry parameters and the lattice Hamiltonian, the optimized lattice Hamiltonian is determined.

[0147] Specifically, lattice symmetry parameters refer to physical quantities that describe the geometric symmetry of a lattice, and are used to characterize the invariance characteristics of a lattice under transformations such as translation, rotation, and reflection. Lattice symmetry parameters include the point group symmetry of the lattice (such as the rotational symmetry axis and mirror plane), the space group symmetry (a combination of translational symmetry and point group), and the like. For example, a two-dimensional square lattice has four-fold rotational symmetry and mirror symmetry, and a honeycomb lattice has six-fold rotational symmetry. The lattice symmetry parameters are automatically derived by the lattice basis vector definition module 10 based on the input basis vector parameters (such as the primitive cell basis vector list and the lattice type). For example, when the user selects a square lattice, the system assumes that it has the symmetry parameters of a square symmetry group.

[0148] Lattice symmetry parameters can be used to simplify the calculation of the lattice Hamiltonian, utilizing symmetry to reduce the number of independent matrix elements and lower the computational complexity.

[0149] An optimized lattice Hamiltonian is a matrix obtained by simplifying or transforming the lattice Hamiltonian based on lattice symmetry parameters, resulting in a matrix with fewer independent parameters or a more compact form. The optimization logic for an optimized lattice Hamiltonian is to reduce the initial matrix (composed of transition and interaction matrix elements) by exploiting lattice symmetries (such as translational and rotational symmetries). For example, for a lattice with translational symmetry, the Hamiltonian can be converted from real space to momentum space via Fourier transform, and then simplified to a block diagonal matrix (each block corresponds to a momentum component) using Bloch's theorem.

[0150] In this way, the lattice structure data includes lattice symmetry parameters, and the Hamiltonian generation module can determine the optimized lattice Hamiltonian based on the lattice symmetry parameters and the lattice Hamiltonian. In this way, the lattice symmetry parameters can be used to identify redundant elements in the Hamiltonian matrix, thereby reducing the matrix dimension and computational complexity.

[0151] See also Figure 3 In some embodiments, the lattice Hamiltonian automatic generator 100 further includes a quantum cluster method interface module 40, which is configured to:

[0152] Based on the preset quantum cluster method, the formatted Hamiltonian data is determined according to the lattice Hamiltonian.

[0153] Specifically, the quantum cluster method interface module 40 is one of the modules in the lattice Hamiltonian automatic generator 100. It is responsible for passing the generated lattice Hamiltonian to the quantum cluster method (QCM) for subsequent calculation and analysis. It is a bridge connecting the Hamiltonian generation with the actual physical simulation, realizing the docking of the lattice Hamiltonian and the QCM method, and ensuring the compatibility of data format and calculation process.

[0154] Pre-defined quantum cluster methods are pre-integrated quantum cluster theory computational methods for addressing many-body problems in strongly correlated electron systems. These include Cluster Perturbation Theory (CPT), Variational Cluster Approximation (VCA), and Cellular Dynamical Mean Field Theory (CDMFT). The Quantum Cluster Method Interface Module 40 provides quantum cluster methods with varying accuracy and computational cost, allowing users to select the method based on their needs.

[0155] Formatted Hamiltonian data refers to data obtained by converting or preprocessing the lattice Hamiltonian according to the input requirements of the preset quantum cluster method. The quantum cluster method interface module 40 converts the lattice Hamiltonian into formatted Hamiltonian data, ensuring that the lattice Hamiltonian can be correctly read and processed by the QCM method, avoiding calculation errors caused by incompatible data formats.

[0156] The quantum cluster method interface module 40 acts as a carrier, calls the preset quantum cluster method, and processes the lattice Hamiltonian into formatted Hamiltonian data, thereby realizing the complete process from automatic generation of Hamiltonian to numerical simulation of multi-body system.

[0157] Thus, the lattice Hamiltonian automatic generator also includes a quantum cluster method interface module, which determines the formatted Hamiltonian data based on the lattice Hamiltonian, based on a pre-set quantum cluster method. This module converts the automatically generated lattice Hamiltonian into the formatted data required by the pre-set quantum cluster method, ensuring that the Hamiltonian data can be directly input into subsequent calculation processes, reducing the tedious manual format conversion process.

[0158] In certain embodiments, during the automatic generation of the lattice Hamiltonian, basis vector parameters, atom types, spin states, supercell lattice vectors, and / or Hamiltonian type may be adjusted.

[0159] Specifically, any one or more of the parameters input by the user, such as basis vector parameters, atom type, spin state, supercell lattice vector, and Hamiltonian type, can be adjusted.

[0160] Users can change the geometric configuration of the lattice (such as switching from a two-dimensional square lattice to a honeycomb lattice) or the physical properties (such as changing from a finite lattice to an infinite lattice) by modifying the basis vector parameters to meet the needs of different material models.

[0161] By adjusting the atomic type and spin state, it can be used to simulate different particle systems (such as electrons, photons) or spin-related physical phenomena (such as ferromagnetism and spin polarization).

[0162] By adjusting the supercell lattice vector, the size and shape of the supercell can be changed (for example, from a 1×1 unit cell to a 2×2 or orthorhombic configuration) to study electron correlation effects at different scales.

[0163] Switching between different Hamiltonian types allows us to study different physical problems (e.g., switching from electron transport to magnetic systems). For example, the Hubbard model focuses on electron hopping and Coulomb interactions, while the Heisenberg model focuses on spin exchange interactions.

[0164] See also Figure 4 , Figure 4 Schematic diagram of the process flow for building the lattice Hamiltonian. The elliptical box is used to indicate the lattice basis vector definition module 10, the rectangular box is used to indicate the lattice filling module 20, the parallelogram box is used to indicate the Hamiltonian generation module 30, and the diamond is used to indicate the quantum cluster method interface module 40. The input of the lattice basis vector definition module 10 is the user-defined basis vector parameters, and the output is the unit cell and lattice structure data. The input of the lattice filling module 20 is the lattice structure data generated by the lattice basis vector definition module 10 and the user-input atom type, spin state, and supercell lattice vector. The output is the lattice filling result, that is, the lattice filling information and supercell definition information. The input of the Hamiltonian generation module 30 is the lattice structure data, the lattice filling result, and the user-input Hamiltonian type, and the output is the lattice Hamiltonian. The input of the quantum cluster method interface module 40 is the lattice Hamiltonian, and the output is the formatted Hamiltonian data and QCM calculation results.

[0165] In this way, during the automatic generation of the lattice Hamiltonian, the basis vector parameters, atom types, spin states, supercell lattice vectors, and / or Hamiltonian type can be adjusted. This allows for the adaptation of lattice models from simple to complex through multi-parameter adjustment, meeting diverse needs.

[0166] See also Figure 5 The embodiment of the present application provides a method for automatically generating a lattice Hamiltonian. The method is based on the above-mentioned lattice Hamiltonian automatic generator and includes:

[0167] 01: Based on the lattice basis vector definition module, the input basis vector parameters are programmatically parsed to generate primitive cells and lattice structure data;

[0168] 02: Based on the lattice filling module, fill the primitive cells with lattice points according to the lattice structure data and determine the lattice filling results;

[0169] 03: Based on the Hamiltonian generation module, the lattice Hamiltonian is automatically generated according to the lattice structure data and lattice filling results.

[0170] The embodiment of the present application also provides a computer device, including a memory and a processor. The task processing method of the embodiment of the present application can be implemented by the computer device of the embodiment of the present application. Specifically, a computer program is stored in the memory, and the processor is used to perform programmatic analysis of the input basis vector parameters based on the lattice basis vector definition module to generate primitive cells and lattice structure data. And based on the lattice filling module, the primitive cells are lattice filled according to the lattice structure data to determine the lattice filling results. And based on the Hamiltonian generation module, the lattice Hamiltonian is automatically generated according to the lattice structure data and the lattice filling results.

[0171] The lattice Hamiltonian automatic generation method of the embodiment of the present application can be implemented by the lattice Hamiltonian automatic generator of the embodiment of the present application. Specifically, the lattice Hamiltonian automatic generator includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module. Based on the lattice basis vector definition module, the input basis vector parameters are programmatically parsed to generate primitive cells and lattice structure data. Then, based on the lattice point filling module, the primitive cells are lattice filled according to the lattice structure data, and the lattice filling results are determined. Finally, based on the Hamiltonian generation module, the lattice Hamiltonian is automatically generated according to the lattice structure data and the lattice point filling results.

[0172] Specifically, the automatic generation method of the lattice Hamiltonian provided in the embodiment of the present application is described below with an example.

[0173] Suppose the user wants to use QCM to study the time-dependent evolution of the Hubbard model in a two-dimensional square lattice system. The system Hamiltonian can be written as:

[0174]

[0175] Among them, i and j are the neighboring lattice points in the model; t is the tunneling strength (transition energy), which characterizes the neighboring lattice points ( ) The ability of electrons to transition between is the electron spin quantum number; Represents the spin The generation operator of the electron at lattice point i; Represents the spin The annihilation operator of the electron at lattice point j; is the Hermitian conjugate term, which ensures that the Hamiltonian is a Hermitian operator (a necessary condition for physical observables), corresponding to the conjugate symmetric part of the transition term; U is the local Coulomb interaction strength, which describes the repulsion between electrons with different spins on the same lattice point; u is the chemical potential, which is used to regulate the number of particles in the system; is the number operator of particles with spin up at lattice point i; is the number operator of particles with spin down at lattice point i; is the total particle number operator on the grid point i ( ).

[0176] Assuming tunneling strength t = -1, interaction strength U = 0.5, and chemical potential u = -1, the system performs the following steps:

[0177] First, in the lattice basis vector definition module, enter the primitive cell parameters. The primitive cell dimension is 2, the vector of each dimension is (1, 0), (0, 1), and there is one lattice point in each primitive cell. Enter the lattice parameters. The lattice is the default two-dimensional square lattice (the lattice vectors of the two dimensions are (1, 0), (0, 1)). The lattice is an infinite lattice, and the boundary condition is an open boundary condition.

[0178] Next, in the lattice filling module, define the lattice points in each unit cell in the lattice model to be filled with spin-free fermions. The user can define the size of the supercell, such as defining the superlattice vectors (1, 0), (0, 1).

[0179] Then, the Hamiltonian generation module constructs the lattice Hamiltonian. According to the Hamiltonian generator, the lattice Hamiltonian with superlattice vectors (1, 0) and (0, 1) can be obtained as follows:

[0180]

[0181] The superlattice vector is ( , ), ( ,- ) is the lattice Hamiltonian:

[0182]

[0183] Finally, the lattice Hamiltonian is passed to the quantum cluster method interface module, and the eigenenergy is calculated by diagonalization through energy spectrum analysis, and the program automatically outputs the calculation results.

[0184] In summary, the lattice basis vector definition module performs programmatic parsing of the input basis vector parameters to generate the primitive cell and lattice structure data. Next, the lattice filling module performs lattice filling of the primitive cell based on the lattice structure data, and the lattice filling results are determined. Finally, the Hamiltonian generation module automatically generates the lattice Hamiltonian based on the lattice structure data and lattice filling results. This automation and modularization of the lattice Hamiltonian generation process avoids the frequent manual intervention required in traditional lattice Hamiltonian construction, thereby improving the efficiency and accuracy of lattice Hamiltonian construction.

[0185] In the description of this specification, the descriptions with reference to the terms "particularly", "further", "particularly", "understandably", etc. are intended to mean that the specific features, structures, materials or characteristics described in conjunction with the embodiments or examples are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms are not intended to refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0186] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0187] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A lattice Hamiltonian automatic generator, characterized in that: The lattice Hamiltonian automatic generator includes a lattice basis vector definition module, a lattice point filling module and a Hamiltonian generation module; The lattice basis vector definition module is configured to perform programmatic analysis on input basis vector parameters to generate primitive cells and lattice structure data; The grid filling module is configured to: Performing lattice filling on the primitive cell according to the input atomic type and spin state, and the lattice type, primitive cell basis vector list, and lattice point coordinate list in the lattice structure data, and determining initial lattice point filling information; Determining grid point filling information in a grid point filling result according to the initial grid point filling information; Determining supercell definition information in the lattice filling result according to the lattice type in the lattice structure data and the input supercell lattice vector, wherein the supercell lattice vector is represented by the primitive cell basis vector list; The Hamiltonian generation module is configured as follows: Determining a zero matrix according to the grid filling result and the input Hamiltonian type; Determining transition matrix elements according to the zero matrix, the primitive cell basis vector list in the lattice structure data, the supercell lattice vectors and input transition parameters; determining interaction matrix elements according to the grid filling result and the input interaction parameters; The lattice Hamiltonian is determined based on the transition matrix element and the interaction matrix element.

2. The lattice Hamiltonian automatic generator according to claim 1, characterized in that: The basis vector parameters include the cell body dimensions of the primitive cell, a primitive cell basis vector list, a lattice coordinate list, a lattice type, a lattice vector list, a lattice size flag, a lattice length and / or a boundary condition type. The lattice basis vector definition module is configured to: Determine the primitive cell according to the cell body dimension, the primitive cell basis vector list and the grid point coordinate list; determining lattice configuration data according to the lattice type and the lattice vector list; determining lattice physical property data according to the lattice size flag, the lattice length and / or the boundary condition type; The lattice structure data is determined according to the unit cell, the lattice configuration data and the lattice physical property data.

3. The lattice Hamiltonian automatic generator according to claim 2, characterized in that: The lattice basis vector definition module is configured as follows: In response to a lattice configuration selection operation, the lattice configuration data is determined from a preset lattice configuration template, wherein the preset lattice configuration template includes a chain lattice, a square lattice, a triangle lattice, a honeycomb lattice, and a cage lattice.

4. The automatic lattice Hamiltonian generator according to claim 1, characterized in that: The grid filling module is configured to: In the case where a defect needs to be constructed for the primitive cell, determining the grid point filling information according to the initial grid point filling information, the input defect primitive cell coordinate list and the defect type; Without constructing defects in the primitive cells, the initial grid point filling information is determined as the grid point filling information.

5. The lattice Hamiltonian automatic generator according to claim 1, characterized in that: The lattice structure data includes lattice symmetry parameters, and the Hamiltonian generation module is configured to: An optimized lattice Hamiltonian is determined according to the lattice symmetry parameters and the lattice Hamiltonian.

6. The automatic lattice Hamiltonian generator according to claim 1, characterized in that: The lattice Hamiltonian automatic generator further includes a quantum cluster method interface module, which is configured to: Based on a preset quantum cluster method, formatted Hamiltonian data is determined according to the lattice Hamiltonian.

7. The automatic lattice Hamiltonian generator according to claim 6, characterized in that: During the automatic generation of the lattice Hamiltonian, the basis vector parameters, the atom type, the spin state, the supercell lattice vector and / or the Hamiltonian type may be adjusted.

8. A method for automatically generating a lattice Hamiltonian, characterized in that: The method is based on the lattice Hamiltonian automatic generator according to claim 1, and the method comprises: Based on the lattice basis vector definition module, the input basis vector parameters are programmatically parsed to generate primitive cell and lattice structure data; Based on the lattice filling module, the lattice filling is performed on the primitive cell according to the input atomic type and spin state, and the lattice type, primitive cell basis vector list and lattice coordinate list in the lattice structure data, to determine initial lattice filling information; Determining, based on the grid point filling module and according to the initial grid point filling information, grid point filling information in a grid point filling result; Determining, based on the lattice filling module, supercell definition information in the lattice filling result according to the lattice type in the lattice structure data and the input supercell lattice vector, wherein the supercell lattice vector is represented by the primitive cell basis vector list; Determining a zero matrix based on the Hamiltonian generation module according to the grid filling result and the input Hamiltonian type; Determining, based on the Hamiltonian generation module, transition matrix elements according to the zero matrix, the primitive cell basis vector list in the lattice structure data, the supercell lattice vectors, and input transition parameters; Determining interaction matrix elements based on the Hamiltonian generation module according to the grid filling result and input interaction parameters; Based on the Hamiltonian generation module, the lattice Hamiltonian is determined according to the transition matrix element and the interaction matrix element.

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