Locality of temperature

TL;DR

This paper extends the concept of temperature to interacting quantum systems by establishing a local definition, demonstrating exponential decay of correlations, and showing stability and efficient approximation of local states above a critical temperature.

Contribution

It introduces a perturbation formula for thermal states and proves exponential clustering, enabling a local understanding of temperature in quantum many-body systems.

Findings

Exponential decay of correlations above a universal critical temperature.

Thermal states are stable against distant perturbations above the critical temperature.

Local expectation values can be efficiently approximated in large systems.

Abstract

This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of "intensivity of temperature" to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size.