Properties of thermal quantum states: locality of temperature, decay of correlations, and more

TL;DR

This paper reviews key properties of thermal quantum states in spin systems, emphasizing quantum information tools to analyze correlations, stability, locality of temperature, and classical simulation, highlighting recent advances.

Contribution

It synthesizes recent results on thermal states' correlation decay, stability, and classical simulability, with a focus on quantum information approaches.

Findings

Finite correlation length states have specific energy distributions.

Canonical and microcanonical ensembles are equivalent for these states.

Thermal states exhibit locality of temperature and stability against perturbations.

Abstract

We review several properties of thermal states of spin Hamiltonians with short range interactions. In particular, we focus on those aspects in which the application of tools coming from quantum information theory has been specially successful in the recent years. This comprises the study of the correlations at finite and zero temperature, the stability against distant and/or weak perturbations, the locality of temperature and their classical simulatability. For the case of states with a finite correlation length, we overview the results on their energy distribution and the equivalence of the canonical and microcanonical ensemble.