Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior

TL;DR

This paper investigates the post-quench dynamics of the quantum Ising chain, revealing that non-local operators exhibit effective thermal behavior while local operators do not, highlighting the role of operator locality and integrability.

Contribution

It demonstrates how operator locality influences thermalization in integrable quantum systems and analyzes the robustness of these features against integrability-breaking perturbations.

Findings

Order parameter correlators decay exponentially with an effective temperature.

Local correlators decay as power-laws and do not thermalize.

Non-local operators exhibit thermal behavior consistent with equilibrium laws.

Abstract

We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior, i.e., they decay exponentially to zero, with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power-law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasi-particles of the model: non-local operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analizing their robustness with respect to a sufficiently strong integrability-breaking term.