Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain

TL;DR

This paper investigates the non-equilibrium dynamics of the quantum Ising chain after a quench, revealing observable-dependent effective temperatures that challenge traditional thermalization concepts.

Contribution

It demonstrates the emergence of observable-dependent effective temperatures in a critical quantum Ising chain, providing insights into non-equilibrium thermalization processes.

Findings

Observable-dependent effective temperatures emerge after a quench.

Gibbs thermalization is not strictly achieved in the studied system.

Distinct effective temperatures may have thermodynamic relevance.

Abstract

Dynamic correlation and response functions of classical and quantum systems in thermal equilibrium are connected by fluctuation-dissipation theorems, which allow an alternative definition of their (unique) temperature. Motivated by this fundamental property, we revisit the issue of thermalization of closed many-body quantum systems long after a sudden quench, focussing on the non-equilibrium dynamics of the Ising chain in a critical transverse field. We show the emergence of distinct observable-dependent effective temperatures, which rule out Gibbs thermalization in a strict sense but might still have a thermodynamic meaning.