# Many-body dynamical localization in the kicked Bose-Hubbard chain

## TL;DR

This paper demonstrates that a kicked Bose-Hubbard model can exhibit a many-body localized phase with ergodicity breaking, non-thermal behavior, and space-delocalized yet sector-localized Floquet states, preventing thermalization.

## Contribution

It provides evidence for a many-body dynamical localization phase in a clean kicked Bose-Hubbard model, highlighting properties distinct from traditional many-body localization.

## Key findings

- Ergodicity breaking persists at large system sizes.
- Floquet states violate eigenstate thermalization hypothesis.
- Local observables depend on initial states and do not thermalize.

## Abstract

We provide evidence that a clean kicked Bose-Hubbard model exhibits a many-body dynamically localized phase. This phase shows ergodicity breaking up to the largest sizes we were able to consider. We argue that this property persists in the limit of large size. The Floquet states violate eigenstate thermalization and then the asymptotic value of local observables depends on the initial state and is not thermal. This implies that the system does not generically heat up to infinite temperature, for almost all the initial states. Differently from many-body localization here the entanglement entropy linearly increases in time. This increase corresponds to space-delocalized Floquet states which are nevertheless localized across specific subsectors of the Hilbert space: In this way the system is prevented from randomly exploring all the Hilbert space and does not thermalize.