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In this work, we develop a stochastic matrix product state (stoMPS) approachthat combines the MPS technique and Monte Carlo samplings and can be applied tosimulate quantum lattice models down to low temperature. In particular, weexploit a procedure to unbiasedly sample the local tensors in the matrixproduct states, which has one physical index of dimension $d$ and two geometricindices of dimension $D$, and find the results can be continuously improved byenlarging $D$. We benchmark the methods on small system sizes and then comparethe results to those obtained with minimally entangled typical thermal states,finding that stoMPS has overall better performance with finite $D$. We furtherexploit the MPS sampling to simulate long spin chains, as well as thetriangular and square lattices with cylinder circumference $W$ up to 4. Ourresults showcase the accuracy and effectiveness of stochastic tensor networksin finite-temperature simulations.

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