Weak ergodicity breaking through the lens of quantum entanglement

TL;DR

This paper introduces the concept of weak ergodicity breaking in quantum many-body systems, highlighting how certain non-thermal eigenstates and slow relaxations are analytically constructed and experimentally observed, challenging traditional thermalization.

Contribution

It provides a pedagogical overview of weak ergodicity breaking, including Hilbert space fragmentation and quantum many-body scars, using quantum entanglement tools for analytical insights.

Findings

Identification of non-thermal eigenstates in non-integrable models

Analytical construction of scars using entanglement techniques

Experimental evidence of weak ergodicity breaking in Rydberg atoms

Abstract

Recent studies of interacting systems of quantum spins, ultracold atoms and correlated fermions have shed a new light on how isolated many-body systems can avoid rapid equilibration to their thermal state. It has been shown that many such systems can "weakly" break ergodicity: they possess a small number of non-thermalising eigenstates and/or display slow relaxation from certain initial conditions, while majority of other initial states equilibrate fast, like in conventional thermalising systems. In this chapter, we provide a pedagogical introduction to weak ergodicity breaking phenomena, including Hilbert space fragmentation and quantum many-body scars. Central to these developments have been the tools based on quantum entanglement, in particular matrix product states and tangent space techniques, which have allowed to analytically construct non-thermal eigenstates in various non-integrable quantum models, and to explore semiclassical quantisation of such systems in the absence of a large-N or mean field limit. We also discuss recent experimental realisations of weak ergodicity breaking phenomena in systems of Rydberg atoms and tilted optical lattices.