Advances in Theoretical and Mathematical Physics
Volume 15 (2011)
Riemann-Hilbert approach to the time-dependent generalized sine kernel
Pages: 1655 – 1743
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 six-vertex 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.