Integro-difference equation for a correlation function of the spin-12 Heisenberg XXZ chain Original Research Article

We consider the Ferromagnetic-String-Formation-Probability correlation function (FSFP) for the spin-12 Heisenberg XXZ chain. We construct , completely integrable system of integro-difference equations (IDE), which has the FSFP as , τ-function. We derive the associated Riemann-Hilbert problem and obtain the long-distance asymptotics of the FSFP correlator in some limiting cases.