Finite-Temperature Simulations of Quantum Lattice Models with Stochastic Matrix Product States

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.