Absence of thermalization of free systems coupled to gapped interacting reservoirs

TL;DR

This study investigates the lack of thermalization in a small XX chain coupled to gapped XXZ leads, revealing persistent oscillations and localized states that challenge the assumption of thermalization in open quantum systems.

Contribution

It demonstrates that gapped interacting reservoirs can prevent thermalization of coupled systems, showing persistent oscillations and localized eigenstates, which is a novel insight into open quantum system dynamics.

Findings

Persistent oscillations are linked to eigenstates within the gap.

Some eigenstates remain localized and do not hybridize.

Gapped leads can prevent thermalization of the central system.

Abstract

We study the thermalization of a small $XX$ chain coupled to long, gapped $XXZ$ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two can not be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the $XX$ chain are related to eigenstates of the entire system located within the gap of the boundary chains. We find from exact diagonalization that some of these states remain strictly localized within the $XX$ chain and do not hybridize with the rest of the system. The frequencies of the persistent oscillations determined by numerical simulations of dynamics match the energy differences between these states exactly. This has important implications for open systems, where the strongly interacting leads are often assumed to thermalize the central system. Our results suggest that if we employ gapped systems for the leads, this assumption does not hold; this finding is particularly relevant to any potential future experimental studies of open quantum systems.