Effective free-fermionic form factors and the XY spin chain

TL;DR

This paper develops effective form factors for 1D lattice fermions with phase shifts, enabling exact summation of tau functions as Fredholm determinants and integrals, and re-derives XY chain correlation asymptotics.

Contribution

It introduces a new method to compute form factors and tau functions for lattice fermions, connecting them to Fredholm determinants and elementary integrals.

Findings

Tau functions expressed as Fredholm determinants in the thermodynamic limit.

Simplified integral representations of form factors.

Re-derivation of XY chain static correlation asymptotics at finite temperature.

Abstract

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.