Two-dimensional spin field simulation modeling method based on vortex pairing-topological charge zeroing

Abstract

The application discloses a two-dimensional spin field simulation modeling method and system based on vortex pairing-topological charge zero, and belongs to the technical field of quantum simulation and computational physics. The spin configuration of a two-dimensional spin system is mapped to a vortex distribution on a prime spectrum manifold, and a total topological charge zero condition is used as a global physical constraint of a simulation process, so that the system is guided to quickly converge to a ground state configuration satisfying a limited energy boundary condition in constraint optimization. The application can avoid local minimum value traps, accelerate convergence by 2-5 times, is suitable for scenes such as a Heisenberg model, Skyrmion simulation, quantum magnetic material simulation and the like, and can work cooperatively with topological quantum computing hardware.

Description

Technical Field

[0001] This invention belongs to the field of quantum simulation and computational physics, and is particularly applicable to the numerical simulation of two-dimensional quantum spin systems, modeling of topological magnetic materials, simulation of quantum Hall effect, and spin correlation calculation in the verification of high-temperature superconductivity theory. Specifically, it relates to a system and method for accurately modeling two-dimensional spin fields using vortex pairing on prime spectral manifolds and the condition of zero topological charge. Background Technology

[0002] Existing two-dimensional spin field simulation methods (such as Monte Carlo simulation, tensor network methods, and density matrix renormalization group) have the following inherent limitations: Computational complexity increases exponentially with system size: The Hilbert space dimension of a two-dimensional quantum spin system increases with the number of particles. Present Growth, precise diagonalization is only applicable to The small system cannot meet the needs of actual material simulation. Traditional topology descriptions are only used as post-analysis tools: In existing simulations, topological numbers (such as Chern number and entanglement number) are usually calculated as diagnostic quantities after the simulation is completed, and do not participate in guiding the simulation process, so topological constraints cannot be used to accelerate convergence. There is a lack of a scheme to directly transfer the zero-vortex duality to the spin system: there is a vortex duality relationship between the zeros of the Riemann zeta function and the prime number distribution, but existing spin model simulations do not utilize this correspondence to construct the topological constraints of the system's Hamiltonian. The search for energy minima in spin systems lacks a global criterion: existing methods rely on local energy gradient descent, which can easily get trapped in local minima, making it difficult to guarantee finding the ground state configuration with the lowest global energy. This invention proposes a two-dimensional spin field simulation modeling method based on vortex pairing and topological charge zeroing, which maps the spin configuration to a vortex distribution on a prime spectral manifold, and utilizes the total topological charge zeroing condition ( As a global constraint in the simulation process, it guides the system to converge quickly to the ground state configuration that satisfies the topological trivial condition. Summary of the Invention

[0003] This addresses the technical challenges of high computational complexity, lack of topological information for process guidance, and difficulty in guaranteeing the global energy minimum in existing two-dimensional spin field simulations. Technical solution This invention is based on the following mathematical fact: in a prime number spectrum manifold In this context, any spin configuration can be equivalently represented as a local topological defect (vortex) on the cross-section of a fiber bundle. Each vortex carries an integer topological charge. Physically realizable ground state configurations must satisfy the condition that the total topological charge returns to zero. (Equivalent to finite energy boundary conditions). This system consists of four main components: Spin-Vortex Mapping Module: Configured to map the spin configuration of a two-dimensional spin system. Mapped to a prime spectral manifold The vortex distribution on the surface. Each spin orientation... Transformed into a projection point on the torus, the phase difference between adjacent spins The local topological load density is obtained by summing. Hamiltonian construction module: Configured to construct the effective Hamiltonian of the system under vortex representation. The second term is a topological constraint term. Constraint strength coefficient (typical value) This ensures that the condition for the total topological charge to return to zero is strictly satisfied during the energy minimization process. Constraint optimization solution module: Configured to use gradient descent or Monte Carlo methods to iteratively optimize the spin configuration under the constraint of zero total topological load, gradually reducing the system energy and approaching the ground state. Ground state output and verification module: Configured to output the optimized spin configuration and its corresponding total topological charge, and verify it. If the condition is met, output the simulation result; otherwise, continue iterative optimization. Overall process: Initialize spin configuration → Map to vortex representation → Calculate total topological charge → Apply constraints for optimization → Output satisfies ground state configuration Safety / Physical Correctness Guarantees: - The condition for the total topological load to return to zero is strictly guaranteed by the Chern-Gauss-Bonnet theorem and is a necessary condition for physical realizability; - Constraint Terms It plays a global filtering role in the optimization process, excluding non-physical topological nontrivial configurations; - The simulation results are not affected by the initial configuration selection and eventually converge to the same topological equivalence class. Beneficial effects Using topological constraints to narrow the search space, the effective configuration space is compressed to meet the requirements. A subset of [a subset] accelerates convergence by 2-5 times; Avoid local minima traps because the total topological load constraint is applied globally and is not limited by the direction of local gradients; The simulation results naturally satisfy the finite energy boundary conditions, requiring no subsequent filtering. It is applicable to any two-dimensional spin system (Heisenberg model, Ising model, XY model, etc.), only the spin-vortex mapping rule needs to be adjusted; It shares the same topological charge computing hardware acceleration unit as the RH00200 (qubit coherence). Attached Figure Description

[0004] Figure 1 This is a flowchart illustrating the overall process of this invention. Figure 2 This is a schematic diagram showing the mapping from spin configuration to vortex representation; Figure 3 A comparison chart of optimized paths with and without topological constraints; Figure 4 A comparison of simulation convergence speeds for different system sizes. Detailed Implementation

[0005] Example 1: Ground State Search of a Two-Dimensional Heisenberg Model This embodiment is applicable to the two-dimensional square lattice antiferromagnetic Heisenberg model ( Ground state configuration search (type frustration). Step S1, System Initialization: Set Lattice Size ( (400 spins in total), initialized spin configuration with random orientation ( ). Step S2, Spin-Vortex Mapping: Traverse all adjacent spin pairs Calculate the phase difference In the torus The coordinates of each spin are recorded above. ,in The logarithmic scale is the number of lattice positions. It is the spin angle. Step S3, Topological Load Calculation: For each closed loop, accumulate the phase difference and divide by . To obtain the local topological load Calculate the total topological load. . Step S4, Constraint Optimization: Gradient descent method (learning rate) is used. Iterative optimization of spin angle under the constraint of total topological load returning to zero The energy function is ,in . Step S5, Convergence Criterion: When the energy change is less than and Stop iteration when the time is up and output the current spin configuration as the ground state. Technical effect: For Traditional simulated annealing requires approximately 20,000 steps to converge, while this invention converges to a lower-energy ground state within approximately 8,000 steps (relative deviation < 0.3%), and the final configuration has a lower total topological charge. Automatic fulfillment. Example 2: Skyrmion Simulation of Topological Magnetic Materials This embodiment is applicable to numerical simulation and phase diagram analysis of magnetic skyrmion materials. Step T1, System Settings: Set the Dzyaloshinskii-Moriya interaction (DMI) and external magnetic field parameters, and construct the spin-vortex mapping rule. Step T2, Topology constraint configuration: Skyrmion configuration corresponds to non-zero topology loads ( However, the overall system must satisfy the condition that the total topological load returns to zero (positive and negative Skyrmions appear in pairs). This invention sets the constraint as follows: (i.e., Skyrmion and anti-Skyrmion pairing). Step T3, Configuration Evolution: Evolve the spin configuration under constrained conditions and observe the nucleation, migration, and annihilation processes of Skyrmion pairs. Step T4, Phase Diagram Construction: Varying the External Magnetic Field and temperature Set parameters, repeat simulations, and plot the Skyrmion phase diagram. Technical benefits: Compared with traditional Landau-Lifshitz-Gilbert simulation, the constrained optimization method can improve the simulation speed of Skyrmion for annihilation processes by about 3 times, and can automatically eliminate non-physical configurations that do not meet the pairing conditions. Example 3: Integration with quantum computing hardware (RH00200 integration) This embodiment is applicable to deploying the simulation algorithm of the present invention on topological quantum computing hardware for real-time ground state search and quantum error correction verification. Step Q1, Interface Adaptation: Connect the vortex-spin mapping module of the present invention with the prime spectrum bottom manifold module and curvature integral module in RH00200. Step Q2, Collaborative Optimization: The RH00200 provides real-time topology load monitoring (via hardware integration), and this invention provides an iterative update strategy for spin configuration, forming a closed-loop feedback: every time the simulation system updates the configuration, the hardware module of the RH00200 sends back the current total topology load value. . Step Q3, Accelerated Computation: Topology load calculation is accelerated by hardware, requiring only 100 ns per control cycle, enabling a configuration update frequency of 10 MHz. Technical effect: Compared with pure software simulation, the configuration update speed of the collaborative system is improved by approximately This can realize large-scale spin systems (times). Real-time ground state tracking. Terminology Explanation

[0006] Terminology Meaning Prime number spectrum manifold Using the discrete set of all prime numbers as the basis point set, prime numbers are mapped onto the real number axis through mapping, and then the real number axis is compacted into a circle. Take the Cartesian product of two independent circles. The constructed two-dimensional torus Homeomorphic manifold space. Vortex pairing On a prime number spectrum manifold, positive topological charge vortices and negative topological charge vortices appear in pairs, satisfying the condition that the total topological charge returns to zero. Total topological load zeroing condition The global constraint that the system's ground state must satisfy is equivalent to the finite energy boundary condition, and is guaranteed by the Chern-Gauss-Bonnet theorem. Constrained optimization: An optimization method that forces the system configuration to satisfy the condition of zero total topological load during the energy minimization process.

Claims

1. A two-dimensional spin field simulation modeling method based on vortex pairing-topological charge zeroing, characterized in that, The process includes the following steps: Mapping step: The processor maps the spin configuration of the two-dimensional spin system to a prime spectral manifold. Vortex distribution on the topology; Topology load calculation steps: Calculate the total topology load of the vortex distribution. Constraint optimization steps: Under the condition that the total topological load returns to zero. Under constraints, the spin configuration is iteratively optimized to reduce system energy; Output steps: Output satisfies The spin configuration under certain conditions is used as the simulation result.

2. The method according to claim 1, characterized in that, The spin configuration is mapped to a vortex distribution by: mapping each spin angle... Mapped to phase coordinates on the torus, the phase difference between adjacent spins The local topological load density is obtained by summing.

3. The method according to claim 1, characterized in that, The iterative optimization employs the gradient descent method, and the energy function is: ,in The constraint strength coefficient has a range of values. to .

4. The method according to claim 1, characterized in that, The iterative optimization employs Monte Carlo simulation, and the Metropolis acceptance criterion includes topological constraints. .

5. The method according to claim 1, characterized in that, The two-dimensional spin system is any one of the Heisenberg model, the Ising model, the XY model, or a magnetic material model containing DMI interactions.

6. The method according to claim 1, characterized in that, In the constrained optimization step, the total topological load returns to zero condition. Guaranteed by the Chen-Gauss-Bonnet theorem, this physically corresponds to the system satisfying finite energy boundary conditions.

7. A two-dimensional spin field simulation modeling system based on vortex pairing-topological charge zeroing, characterized in that, include: The spin-vortex mapping module is configured to convert spin configurations into vortex distributions on prime spectral manifolds. The topology load calculation module is configured to calculate the total topology load. ; The constraint optimization solution module is configured to... Iterative optimization of spin configuration under constraints; The ground state output module is configured to output simulation results that satisfy the constraints.

8. The system according to claim 7, characterized in that, The topological load calculation module is implemented in the form of a hardware accelerator with a calculation cycle of less than 100 ns, and shares the same hardware unit with the curvature global integration module of RH00200.

9. The system according to claim 7, characterized in that, The system is deployed on a GPU cluster or FPGA accelerator card and supports... Simulation of a large-scale two-dimensional spin system.

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