The Luttinger model following a sudden interaction switch-on

TL;DR

This paper analytically investigates how correlations evolve in the exactly solvable Luttinger model after a sudden interaction switch-on, revealing periodic behavior in finite systems and algebraic relaxation to a generalized Gibbs ensemble in the thermodynamic limit.

Contribution

It provides an exact analytical study of the non-equilibrium dynamics of the Luttinger model following a sudden interaction quench, including the characterization of correlation decay and relaxation.

Findings

Correlations are periodic in finite-size systems at zero temperature.

In the thermodynamic limit, correlations relax algebraically to a generalized Gibbs ensemble.

The decay exponent of the one-particle correlation differs from equilibrium exponents.

Abstract

The evolution of correlations in the \emph{exactly} solvable Luttinger model (a model of interacting fermions in one dimension) after a sudden interaction switch-on is \emph{analytically} studied. When the model is defined on a finite-size ring, zero-temperature correlations are periodic in time. However, in the thermodynamic limit, the system relaxes algebraically towards a stationary state which is well described, at least for some simple correlation functions, by the generalized Gibbs ensemble recently introduced by Rigol \emph{et al.} [cond-mat/0604476]. The critical exponent that characterizes the decay of the one-particle correlation function is different from the known equilibrium exponents. Experiments for which these results can be relevant are also discussed.