Riemann-Hilbert approach to the time-dependent generalized sine kernel

Abstract

We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance-dependent correlation functions of integrable models described by a sixvertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. © 2011 International Press.