Decay of Correlations in Fermi Systems at Non-zero Temperature

TL;DR

This paper demonstrates that in Fermi systems at non-zero temperature, correlation functions decay exponentially with a correlation length inversely proportional to temperature, impacting numerical simulations.

Contribution

It establishes the exponential decay of correlations in Fermi systems at finite temperature for short-range lattice Hamiltonians, linking correlation length to inverse temperature.

Findings

Correlation functions decay exponentially at non-zero temperature.

Correlation length is proportional to inverse temperature.

Implications for numerical simulation accuracy.

Abstract

The locality of correlation functions is considered for Fermi systems at non-zero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at non-zero temperature.