Universal correlations of one-dimensional interacting electrons in the gas phase

TL;DR

This paper investigates the dynamical correlation functions of one-dimensional interacting electrons at finite temperature, identifying a universal model for the gas phase and providing exact asymptotic expressions under various conditions.

Contribution

It introduces the impenetrable electron gas model as a universal framework for the gas phase of 1D electrons and derives explicit asymptotic correlation functions at low temperatures.

Findings

Correlation functions are explicitly calculated for the gas phase.

The model applies universally below a critical chemical potential.

Exact asymptotics are obtained in magnetic fields.

Abstract

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.