Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

TL;DR

This paper examines how the generalized Gibbs ensemble describes the long-term behavior of the quantum Ising chain after a quench, highlighting the impact of translational invariance breaking and disorder.

Contribution

It demonstrates that breaking translational invariance invalidates the generalized Gibbs ensemble's applicability in finite systems, especially with disorder, contrasting prior assumptions of its universal validity.

Findings

GGE accurately describes asymptotic correlations in translationally invariant systems.

Breaking translational invariance disrupts GGE validity in finite systems.

Disorder significantly affects the applicability of GGE after a quench.

Abstract

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench of the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g., by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder.