One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations

TL;DR

This paper derives the large-distance asymptotics of correlation functions for impenetrable anyons at finite temperature, revealing their behavior through nonlinear PDEs and Riemann-Hilbert analysis, and connecting results to free fermions, bosons, and conformal field theory.

Contribution

It introduces a method to analyze space correlations of impenetrable anyons using differential equations and Riemann-Hilbert problems, extending known results for bosons and fermions.

Findings

Asymptotic formulas match free fermions and bosons in specific limits

Exponential and pre-exponential factors in correlator asymptotics are calculated

Results agree with conformal field theory predictions at low temperatures

Abstract

Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely characterizing the correlators. The system is the same as the one for impenetrable bosons but with different initial conditions. The large-distance asymptotic behavior of the correlation functions is obtained from the analysis of the Riemann-Hilbert problem associated with the system of differential equations. We calculate both the exponential and pre-exponential factors in the asymptotics of the field-field correlators. The asymptotics derived in this way agree with those of the free fermions and impenetrable bosons in the appropriate limits, $\kappa\to 1$ and $\kappa\to 0$, of the statistics parameter $\kappa$, and coincide with the predictions of the conformal field theory at low temperatures.