Correlations in the impenetrable electron gas

TL;DR

This paper analyzes the long-distance and long-time behavior of correlation functions in a one-dimensional impenetrable electron gas, revealing how strong interactions influence asymptotic decay at various temperatures.

Contribution

It provides exact asymptotic formulas for correlation functions in the impenetrable electron gas, including temperature effects and interaction corrections, extending previous understanding of such strongly correlated systems.

Findings

Exponential decay of correlators characterized

Power law corrections identified

Results valid at all temperatures, simplifying at low T

Abstract

We consider non-relativistic electrons in one dimension with infinitely strong repulsive delta function interaction. We calculate the long-time, large-distance asymptotics of field-field correlators in the gas phase. The gas phase at low temperatures is characterized by the ideal gas law. We calculate the exponential decay, the power law corrections and the constant factor of the asymptotics. Our results are valid at any temperature. They simplify at low temperatures, where they are easily recognized as products of free fermionic correlation functions with corrections arising due to the interaction.