Quantum quench dynamics of some exactly solvable models in one dimension

The dynamics of the Luttinger model and the sine-Gordon model (at the Luther-Emery point and in the semiclassical approximation) after a quantum quench is studied. We compute in detail one and two-point correlation functions for different types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa, and from the gapped to the gapless phase of the sine-Gordon model and vice-versa. A progressive destruction of the Fermi gas features in the momentum distribution is found in the case of a quench into an interacting state in the Luttinger model. The critical exponents for spatial correlations are also found to be different from their equilibrium values. Correlations following a quench of the sine-Gordon model from the gapped to the gapless phase are found in agreement with the predictions of Calabrese and Cardy [Phys. Rev. Lett. {\bf 96} 136801 (2006)]. However, correlations following a quench from the gapped to the gapless phase at the Luther-Emery and the semi-classical limit exhibit a somewhat different behavior, which may indicate a break-down of the semiclassical approximation or a qualitative change in the behavior of correlations as one moves away from the Luther-Emergy point. In all cases, we find that the correlations at infinite times after the quench are well described by a generalized Gibbs ensemble [M. Rigol \emph{et al.} Phys. Rev. Lett. {\bf 98}, 050405 (2007)], which assigns a momentum dependent temperature to each eigenmode.