Matrix product purifications for canonical ensembles and quantum number distributions

TL;DR

This paper develops efficient methods for computing matrix product purifications of canonical ensembles and quantum number distributions, leveraging symmetries to improve simulation of quantum many-body systems at finite temperatures.

Contribution

It introduces new techniques for canonical ensemble MPPs with symmetry exploitation and presents a scheme for quantum number distribution evaluation using MPDOs.

Findings

Exact MPP representations for canonical infinite-temperature states.

Demonstration of techniques on Heisenberg spin-1/2 chains.

Energy density differences decay as 1/L between ensembles.

Abstract

Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1/2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1/L.