Integro-Difference Equation for a correlation function of the spin-${1\over2}$ Heisenberg XXZ chain

TL;DR

This paper develops an integrable system of integro-difference equations for the ferromagnetic string formation probability in the spin-1/2 Heisenberg XXZ chain, deriving asymptotics and a Riemann-Hilbert problem.

Contribution

It introduces a novel integrable IDE system with the FSFP as a tau-function, linking correlation functions to integrable systems theory.

Findings

Constructed a new integrable system of IDEs for FSFP

Derived the associated Riemann-Hilbert problem

Obtained large distance asymptotics of the correlator

Abstract

We consider the Ferromagnetic-String-Formation-Probability correlation function (FSFP) for the spin-$1\over 2$ Heisenberg XXZ chain. We construct a completely integrable system of integro-difference equations (IDE), which has the FSFP as a $\tau$-function. We derive the associated Riemann-Hilbert problem and obtain the large distance asymptotics of the FSFP correlator in some limiting cases.