Locally accurate matrix product approximation to thermal states

Abstract

In one-dimensional quantum systems with short-range interactions, a set of leading numerical methods is based on matrix product states, whose bond dimension determines the amount of computational resources required by these methods. We prove that a thermal state at constant inverse temperature ${\hat{I}}^2$ has a matrix product representation with bond dimension $e^{\tilde{O}(\sqrt{{\hat{I}}^2\log (1/\hat{I}\mu )})}$ such that all local properties are approximated to accuracy $\hat{I}\mu$. This justifies the common practice of using a constant bond dimension in the numerical simulation of thermal properties.

v2: abstract and introduction expanded