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.
Highlights
The effects of interactions on disordered localized physical systems remained to a large extent a mystery for over 50 years after the pioneering work of Anderson [1] who introduced the concept of single-particle localization
We have presented a comprehensive analysis of many-body localization for a system of interacting bosons in a lattice in the presence of disorder
We considered both the random chemical potential as well as we revisited the case of random interactions
Summary
The effects of interactions on disordered localized physical systems remained to a large extent a mystery for over 50 years after the pioneering work of Anderson [1] who introduced the concept of single-particle localization. The study of interactions in the metallic regime practically began with the work of Altshuler and Aronov [2], subsequently problems related to the presence of the disorder and interactions were addressed by several works (a highly incomplete list may include [3,4,5,6]) in cold atomic settings [7] It was in the seminal paper [8] that many body localization (MBL) was identified as a genuine new phenomenon occurring for sufficiently strong disorders.
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