F.H.L. Essler, H. Frahm, A.R. Its, V.E. Korepin
Integro-Difference Equation for a correlation function of the
spin-1/2 Heisenberg XXZ chain
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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.