One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions

TL;DR

This paper analyzes the large time and distance asymptotics of correlation functions for impenetrable one-dimensional anyons at finite temperature, revealing deviations from conformal field theory predictions in certain limits.

Contribution

It derives the asymptotic behavior of correlation functions for 1D impenetrable anyons, highlighting differences from conformal predictions at low temperatures and away from bosonic points.

Findings

Asymptotic correlation functions are derived for finite temperature.

Results recover known bosonic and fermionic cases in specific limits.

Leading terms differ from conformal field theory predictions at low temperatures.

Abstract

This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.