Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems

Abstract

In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.

Transport in quasiperiodic interacting systems: From superdiffusion to subdiffusion

“…From the inset, which shows the extracted dynamical exponent, it is clear that there is actually no finite regime of parameters for which the system is diffusive. Similar behavior was observed in an experimental and numerical study, which appeared while this work was in preparation [11]. To verify that the observed behavior occurs also for pure initial states, we calculated the MSD and the entanglement entropy (EE) starting form the Néel state (see Fig.…”

“…5). We note that for the system we study the Néel state is a state with relatively high energy density, lying close to the center of the many-body band, and has been successfully utilized to demonstrate MBL in cold atoms experiments [10,11]. However unlike the experiments, we do not allow volatility in the initial state, namely we have exactly one particle sitting on every other lattice site.…”

“…In the standard quenched disordered variants of such systems, dynamical behavior is observed that exhibits a rich set of distinct transport behaviors [5][6][7][8][9]. Interacting quasiperiodic (QP) systems are also believed to exhibit similar behavior, and are the basis for several recent experimental studies on MBL [10,11]. Unfortunately, very little is known about transport in such systems.…”

Scaling Theory of Entanglement at the Many-Body Localization Transition

“…The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume-law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume-law on the thermal side, to pure area-law on the MBL side.Recent experimental advances in synthesizing isolated quantum many-body systems, such as cold-atoms [1][2][3][4], trapped ions [5,6], or impurity spins in solids [7,8], have raised fundamental questions about the nature of statistical mechanics. Even when decoupled from external sources of dissipation, large interacting quantum systems tend to act as their own heat-baths and reach thermal equilibrium.…”

“…Recent experimental advances in synthesizing isolated quantum many-body systems, such as cold-atoms [1][2][3][4], trapped ions [5,6], or impurity spins in solids [7,8], have raised fundamental questions about the nature of statistical mechanics. Even when decoupled from external sources of dissipation, large interacting quantum systems tend to act as their own heat-baths and reach thermal equilibrium.…”