Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis

TL;DR

This paper demonstrates analytically and numerically that local quenches in XX-spin-chain models can prevent thermalization and strongly violate the eigenstate thermalization hypothesis, even in cases where weaker ETH versions hold.

Contribution

It provides the first analytical proof and numerical evidence that local quenches can cause absence of thermalization and violate ETH more strongly than previously known.

Findings

Absence of thermalization after a local quench in XX-spin-chain models.

Strong violation of the eigenstate thermalization hypothesis (ETH).

Numerical evidence for phenomena in XXZ-models with end-impurities.

Abstract

Absence of thermalization after a global quantum quench is a well-established numerical observation in integrable many-body systems, and can be empirically related to a violation of the eigenstate thermalization hypothesis (ETH) in such models. Still, in many of those examples a weaker version of the conventional ETH (wETH) has been numerically reported or even rigorously proven. In this paper we show analytically and illustrate numerically that the absence of thermalization is already possible after a local quench. A closely related finding is a strong violation of the ETH, meaning that not even the wETH is fulfilled anymore. In our analytical explorations we focus on XX-spin-chain models with open boundary conditions, where the local quench is generated by initiating the system in thermal equilibrium and then suddenly switching on (or slightly changing) a single-spin impurity either at the end or in the center of the chain. Numerically we observe qualitatively similar phenomena also for more general XXZ-models in the case of an end-impurity, but not in the case of a central impurity.