Zero temperature correlation functions for the impenetrable fermion gas

TL;DR

This paper derives the long-time, long-distance asymptotics of one-particle correlation functions in a 1+1D impenetrable spin-1/2 fermion gas at zero temperature, using Riemann-Hilbert problem techniques.

Contribution

It provides the first detailed asymptotic analysis of correlation functions in this model at zero temperature in the spin-disordered regime.

Findings

Asymptotic expressions for correlation functions are obtained.

The analysis employs matrix Riemann-Hilbert problem methods.

Results enhance understanding of quantum correlations in 1D fermionic systems.

Abstract

We calculate the long time and distance asymptotics of the one-particle correlation functions in the model of impenetrable spin 1/2 fermions in 1+1 dimensions. We consider the spin disordered zero temperature regime, which occurs when the limit $T\to0$ is taken at a positive chemical potential. The asymptotic expressions are found from the asymptotic solution of the matrix Riemann-Hilbert problem related to the determinant representation of the correlation functions.