Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons

TL;DR

This paper derives the large time and distance asymptotics of field-field correlators for 1D impenetrable anyons at finite temperature, revealing non-conformal behavior dominated by spectral density singularities.

Contribution

It provides the exact asymptotic behavior of correlators for 1D anyons, highlighting deviations from conformal field theory predictions due to spectral density singularities.

Findings

Asymptotics reproduce known limits for bosons and fermions.

Correlators are dominated by spectral density singularities at the band bottom.

Response to low-energy probes remains conformal despite non-conformal asymptotics.

Abstract

The exact large time and distance behavior of the field-field correlators has been computed for one-dimensional impenetrable anyons at finite temperatures. The result reproduces known asymptotics for impenetrable bosons and free fermions in the appropriate limits of the statistics parameter. The obtained asymptotic behavior of the correlators is dominated by the singularity in the spectral density of the quasiparticle states at the bottom of the band, and differs from the predictions of the conformal field theory. One can argue, however, that the anyonic response to the low-energy probes is still determined by the conformal terms in the asymptotic expansion.