Exact Solution of Riemann–Hilbert Problem
for a Correlation Function of the XY Spin Chain

Abstract

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann–Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.