Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

TL;DR

This paper investigates whether quantum systems, specifically the transverse field Ising chain, exhibit thermal behavior after a quench by analyzing fluctuation-dissipation relations, revealing a lack of thermalization to a Gibbs ensemble.

Contribution

It introduces a method to study effective temperatures in quantum systems post-quench through fluctuation-dissipation relations, highlighting conditions where thermalization does not occur.

Findings

No thermalization to Gibbs ensemble observed

Effective parameters vary with time or frequency

Quantum Ising chain remains out of equilibrium after quench

Abstract

Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time- or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach.