Thermalization in Systems with Bipartite Eigenmode Entanglement

TL;DR

This paper analytically demonstrates that in exactly solvable quantum models, strong bipartite eigenmode entanglement can lead to thermal-like correlations after a quench, with specific conditions determining when this occurs.

Contribution

It identifies conditions under which eigenmode entanglement results in thermal correlations, including the role of energy gaps and the distinction between thermal and non-thermal long-time behavior.

Findings

Thermal correlations emerge from initial states with large energy gaps.

Non-thermal correlations occur when entanglement does not involve a gap.

Asymptotic correlations can differ from true thermal ensembles, shown by energy fluctuation measurements.

Abstract

It is analytically shown that the asymptotic correlations in exactly solvable models following a quantum quench can behave essentially as thermal correlations provided the entanglement between two eigenmodes is sufficiently strong. We provide one example and one counter example of this observation. The example illustrates the fact that the thermal correlations arise from initial states where the entanglement between the eigenmodes stems from the existence of a large energy gap in the initial state. On the other hand, the counter-example shows that when the bi-partite entanglement of the eigenmodes stems from interactions that do not open a gap, the correlations at asymptotically long times are non-thermal. We also show that the thermal behavior concerns only the asymptotic correlation functions, as the difference with an actual thermal ensemble can be observed measuring the energy fluctuations of the system. The latter observation implies a breakdown of the fluctuation-dissipation theorem.