Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas

TL;DR

This paper analyzes the large time and distance asymptotics of thermal correlators in a one-dimensional impenetrable lattice anyonic gas, revealing universal behaviors and connections to quantum spin chains.

Contribution

It introduces an effective form factor approach to describe asymptotics of correlation functions in the model, highlighting differences between space-like and time-like regions.

Findings

Asymptotic behavior differs in space-like and time-like regions.

Time-like region shows additional power-law factor on exponential decay.

Results recover known spin-spin correlation asymptotics at specific parameters.

Abstract

We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large time and long distance behavior of these objects we use effective form factor approach. The asymptotic behavior is different in the space-like and time-like regions. In particular, in the time-like region we observe the additional power factor on top of the exponential decay. We argue that this result is universal as it is related to the discontinuous behavior of the phase shift function of the effective fermions. At particular values of the anyonic parameter we recover asymptotics of spin-spin correlation functions in XXO quantum chain.