Quantum quench dynamics of some exactly solvable models in one dimension

Details Quantum quench dynamics of some exactly solvable models in one dimension Quantum quench dynamics of some exactly solvable models in one dimension

2009-03-06

arxiv.org/abs/0903.1205v2

Phys. Rev. A, 80, 063619 (2009) and arXiv:1003.5167

Physics

Condensed Matter

Strongly Correlated Electrons

24 pages + 3 figures; typos corrected and references added

Scientific paper

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.

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