Time and Temperature Dependent Correlation Functions of 1D Models of Quantum Statistical Mechanics

TL;DR

This paper derives a universal formula for the asymptotic behavior of correlation functions in 1D gapless quantum models at any temperature, revealing exponential decay at finite temperatures and power-law decay at zero temperature.

Contribution

It provides a new, exact formula for long-distance and long-time correlation functions applicable across all temperatures and coupling constants in 1D gapless models.

Findings

Correlation functions decay as power laws at zero temperature.

Correlation functions decay exponentially at finite temperatures.

The derived formula applies to any temperature and coupling constant.

Abstract

We consider gapless models of statistical mechanics. At zero temperatures correlation functions decay asymptotically as powers of distance in these models. Temperature correlations decay exponentially. We used an example of solvable model to find the formula, which describes long distance and large time asymptotic of correlation function of local fields. The formula describes correlation at any temperature and arbitrary coupling constant.