Time and temperature dependent correlation functions of the 1D impenetrable electron gas

TL;DR

This paper analyzes the long-time, large-distance behavior of correlation functions in a 1D impenetrable electron gas at finite temperatures, deriving explicit asymptotic formulas that describe their decay and power-law behavior.

Contribution

It introduces determinant representations and Riemann-Hilbert problem techniques to obtain universal asymptotic formulas for correlation functions at all finite temperatures.

Findings

Correlation functions exhibit power-law and exponential decay.

Explicit asymptotic formulas valid at all finite temperatures.

Behavior depends on temperature, magnetic field, and chemical potential.

Abstract

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann-Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.