Thermal States as Convex Combinations of Matrix Product States

TL;DR

This paper demonstrates that thermal states of quantum spin chains can be expressed as convex combinations of matrix product states, offering insights into entanglement and supporting computational algorithms.

Contribution

It proves that thermal states can be represented as convex combinations of matrix product states, justifying and enhancing existing simulation methods.

Findings

Thermal states are convex combinations of matrix product states.

Supports the use of minimally entangled typical thermal states algorithm.

Provides insights into entanglement structure and dynamical algorithms.

Abstract

We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.