SYMMETRY-ENHANCED NEURAL QUANTUM STATES FOR THE TRANSVERSE FIELD ISING MODEL
งานวิจัยนี้ใช้สถานะนิวรัลควอนตัมเชิงสมมาตร (Symmetric NQS) เพื่อคำนวณหาสถานะพื้นของแบบจำลองไอซิงในสนามแม่เหล็กตามขวางหนึ่งมิติ เราแสดงให้เห็นว่าการบังคับใช้สมมาตร Z2 ของระบบเป็นสิ่งจำเป็นอย่างยิ่งในการได้มาซึ่งผลลัพธ์ที่แม่นยำและมีเสถียรภาพ ซึ่งแก้ปัญหาที่แนวทาง NQS มาตรฐานล้มเหลวในระบบขนาดใหญ่ได้
DOI:
https://doi.org/10.55766/sujst10600Keywords:
Neural Quantum States, Variational Monte Carlo, Transverse Field Ising Model, Spin-flip Symmetry, Quantum Many-Body SystemsAbstract
The quantum many-body problem presents a significant computational challenge due to the exponential scaling of the Hilbert space. In this work, we address this problem by applying Neural Quantum States (NQS) within a Variational Monte Carlo (VMC) framework to determine the ground state of the Transverse Field Ising Model (TFIM) in one dimension. We employ neural network architectures tailored to the system's dimensionality: a Feed-Forward Network for the 1D chain. A key feature of our approach is the explicit enforcement of the global Z2 spin-flip symmetry of the Hamiltonian onto the NQS wavefunction, which restricts the search to the correct physical subspace. We benchmark our results against exact diagonalization for systems of various sizes and model parameters. The calculated ground state energies show excellent agreement with the exact values, with relative errors falling in the range of 0.4% - 0.7%. This study demonstrates that tailored, symmetric NQS are a powerful, accurate, and flexible tool for investigating quantum many-body systems.
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