Uniform-in-temperature locality estimates for weakly interacting quantum systems

TL;DR

This paper proves that certain weakly interacting quantum systems exhibit uniform exponential decay of correlations and local indistinguishability across all temperatures, aiding understanding of thermal states and their simulation.

Contribution

It establishes uniform-in-temperature locality bounds for weakly interacting quantum systems using a novel low-temperature cluster expansion and a quantum swapping technique.

Findings

Exponential decay of correlations holds uniformly in temperature.

Local indistinguishability is maintained across all temperature regimes.

The results apply to a class of weakly interacting quantum Hamiltonians.

Abstract

The locality of thermal quantum states has emerged as a key input for applications to thermalization, response theory, and efficient simulability. Locality is either captured by the decay of correlations or by local indistinguishability, which allows to approximate local expectation values by those of local thermal states. Most techniques for deriving locality bounds deteriorate at small temperature, a physically highly relevant regime and so it is of interest to identify conditions for uniform-in-temperature bounds. Here we prove that a class of weakly interacting quantum Hamiltonians satisfies exponential decay of correlations and local indistinguishability uniformly in the temperature. The proof uses a low-temperature cluster expansion and a quantum version of a probabilistic swapping trick developed by the first author and Cao (Ann. Probab. 53, 2025) in the context of lattice gauge theories.