Many-body localization of bosons in optical lattices

TL;DR

This paper investigates many-body localization in bosonic systems within optical lattices, comparing models with different disorder types, and identifies energy-dependent localization edges and subdiffusive behavior near phase transitions.

Contribution

It introduces a comparative analysis of disorder effects in bosonic optical lattices and reveals energy-dependent localization properties and subdiffusive dynamics near the transition.

Findings

Localization occurs at high disorder levels in both models.

Energy-dependent localization edges are observed.

Subdiffusive behavior appears near the phase transition.

Abstract

Many-body localization for a system of bosons trapped in a one dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.