使用随机矩阵乘积态对量子晶格模型进行有限温度模拟
Finite-Temperature Simulations of Quantum Lattice Models with Stochastic Matrix Product States
AI总结：
本文提出结合MPS与Monte Carlo采样的stoMPS方法，通过无偏采样局域张量实现量子晶格模型的有限温度模拟，并在自旋链与二维晶格上验证其精度和性能。
摘要：
在本工作中，我们开发了一种随机矩阵乘积态（stoMPS）方法，该方法结合了MPS技术与Monte Carlo采样，并可用于模拟直至低温的量子晶格模型。特别地，我们采用一种程序对矩阵乘积态中的局域张量进行无偏采样，这些张量具有一个维数为$d$的物理指标和两个维数为$D$的几何指标，并发现通过增大$D$可以持续改进结果。我们在小系统尺寸上对该方法进行基准测试，随后将结果与使用最小纠缠典型热态所得结果进行比较，发现有限$D$下stoMPS总体上具有更好的性能。我们进一步利用MPS采样模拟长自旋链，以及圆柱周长$W$最大为4的三角晶格和方格。我们的结果展示了随机张量网络在有限温度模拟中的准确性和有效性。
英文摘要：
In this work, we develop a stochastic matrix product state (stoMPS) approach that combines the MPS technique and Monte Carlo samplings and can be applied to simulate quantum lattice models down to low temperature. In particular, we exploit a procedure to unbiasedly sample the local tensors in the matrix product states, which has one physical index of dimension $d$ and two geometric indices of dimension $D$, and find the results can be continuously improved by enlarging $D$. We benchmark the methods on small system sizes and then compare the results to those obtained with minimally entangled typical thermal states, finding that stoMPS has overall better performance with finite $D$. We further exploit the MPS sampling to simulate long spin chains, as well as the triangular and square lattices with cylinder circumference $W$ up to 4. Our results showcase the accuracy and effectiveness of stochastic tensor networks in finite-temperature simulations.
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