Coexistence of localized and extended phases: Many-body localization in a harmonic trap

Abstract

We show that the presence of a harmonic trap may in itself lead to many-body localization for cold atoms confined in that trap in a quasi-one-dimensional geometry. Specifically, the coexistence of delocalized phase in the center of the trap with localized region closer to the edges is predicted with the borderline dependent on the curvature of the trap. The phenomenon, similar in its origin to Stark localization, should be directly observed with cold atomic species. We discuss both the spinless and the spinful fermions; for the latter we address Stark localization at the same time as it has not been analyzed up until now.

Many-body localization regime for cavity induced long-range interacting models

“…First we briefly recall the model and study the time dynamics in the presence of random disorder. Later we consider localization in disorder-free tilted lattice that extends extensive recent studies of such models [51][52][53][54][55][56][57] to infinite range potentials. Let us also note here the recent work [58] which discusses localization in tilted lattice for dipolar i.e., power-law decaying interactions.…”

“…As a second example we consider the case of a harmonic potential on top of the lattice, h i = A 2 (i − i 0 ) 2 , where i 0 denotes the center of the lattice (i 0 = 20.5 for lattice of size L = 40 considered). Such a potential was considered in [54] where we have found that for short-ranged interactions the system splits into separate regions. While at the center the system delocalizes, clear signatures of localization are observed at the outer regions leading to "phase separation" or the coexistence of localized phases with ergodic central bubble.…”

“…6 shows that this is the case also for cavity induced interaction system, (3). To visualize local dynamics we use the concept of local imbalance introduced by us previously [54,57]. In the spin formulation it reads…”

“…Here we limit the evolution to experimentally feasible times of the order of t = 500/J [75]. Furthermore, earlier works [54,57] hinted that for short-ranged interacting systems the transition in space between the localized and delocalized parts of the system depends only on the local effective field value F loc = A(i − i 0 ) irrespective of the curvature value A. To verify this for cavity induced infinite-ranged system, we plot the variations of the long time snapshot of the local imbalance as a function of the local effective field value F loc in Fig.…”

Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping

“…At the same time, a substantial fraction of states in other subspaces are delocalized [38]. Coexistence of localization and delocalization has been demonstrated in a variety of systems with dipole (or higher) moment conservation both numerically [38][39][40][41][42][43][44] and analytically [38,45]. Experimental evidences for the Wannier-Stark localization without disorder were recently reported [1,2,46].…”