Ergodicity breaking with long range cavity induced quasiperiodic interactions

TL;DR

This paper investigates ergodicity breaking and many-body localization in an extended Bose-Hubbard model with long-range quasiperiodic interactions, revealing conditions under which localization persists or gives way to ergodicity.

Contribution

It introduces a model with long-range quasiperiodic interactions without disorder, analyzing localization and ergodicity transitions with potential experimental verification.

Findings

Significant eigenstate localization occurs with strong interactions.

System becomes ergodic in the thermodynamic limit with extensive energy.

Localization remains stable under super-extensive energy scaling.

Abstract

Many-body localization (MBL) behavior is analyzed {in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is present. Examining level statistics and entanglement entropy of eigenstates we show that a significant fraction of eigenstates of the system is localized in the presence of strong interactions. In spite of this, our results suggest that the system becomes ergodic in the standard thermodynamic limit in which the energy of the system is extensive. At the same time, the MBL regime seems to be stable if one allows for a super-extensive scaling of the energy. We show that our findings can be experimentally verified by studies of time dynamics in many-body cavity quantum electrodynamics setups. The "quench spectroscopy" is a particularly effective tool that allows us to systematically study energy dependence of time dynamics and to investigate a mobility edge in our system.