Motivated by recent experiments on non-ergodic phenomenon in quasi-one-dimensional optical lattice, we analyse theoretically properties of the Many-Body Localization (MBL) driven by disorder and curvature. For disorder-driven localization transition, we studied the crossover between localized and delocalized regimes. We defined new observables, the mean speed of transport and edge fluctuations at long times. They give direct probe for mobility edge in energy spectrum. For MBL by curvature, we firstly studied Many-Body Stark Localization (MBSL) and revealed its multifractal character. Then we proposed and analyzed a scenario of coexistence of extended and localized phases by simply harmonic envelope with no disorder. Finally we show it may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

Ruixiao Yao

Peking University