Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures

TL;DR

This paper analyzes the large-distance asymptotic behavior of correlation functions for 1D impenetrable anyons at finite temperatures, confirming conformal field theory predictions and deriving a system of differential equations characterizing these correlations.

Contribution

It introduces a new integrable system of differential equations that fully describes the 2-point correlation functions of 1D impenetrable anyons at finite temperatures.

Findings

Asymptotic behavior matches conformal field theory at low temperatures.

Reproduces known results for bosons and fermions in special limits.

Derives a differential equation system for correlation functions.

Abstract

The large-distance asymptotic behavior of the field-field correlators has been computed for one-dimensional impenetrable anyons at finite temperatures. The asymptotic behavior agrees with the predictions of conformal field theory at low temperatures and reproduces the known results for impenetrable bosons and free fermions in appropriate limits. We have also obtained an integrable system of partial nonlinear differential equations which completely characterizes the 2-point correlation functions. The system is the same as for bosons but with different initial conditions.