Memory-preserving equilibration after a quantum quench in a 1d critical model

TL;DR

This paper demonstrates that in a 1D critical quantum system, the system retains extensive memory of its initial state after a quench, challenging the adequacy of the standard Gaussian GGE in describing such equilibration.

Contribution

It reveals that non-Gaussian initial correlations persist in the long-time limit, showing limitations of the Gaussian GGE in non-Gaussian initial states within gapless integrable systems.

Findings

Memory of non-Gaussian correlations is preserved after a quench.

Standard GGE fails to predict local observables for non-Gaussian initial states.

Proposes experimental test to observe GGE failure in non-Gaussian initial conditions.

Abstract

One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general one-dimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.