Quantum quench dynamics of some exactly solvable models in one dimension

TL;DR

This paper investigates the non-equilibrium dynamics of exactly solvable 1D models after quantum quenches, analyzing correlation functions and the applicability of generalized Gibbs ensembles in describing long-time behavior.

Contribution

It provides detailed calculations of correlation functions in quenched Luttinger and sine-Gordon models, highlighting differences from equilibrium and the role of generalized Gibbs ensembles.

Findings

Fermi gas features diminish after quenches into interacting states.

Critical exponents for correlations differ from equilibrium values.

Long-time correlations are well described by a generalized Gibbs ensemble.

Abstract

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.