Slow Dynamics near the Many-Body Localization Transition

We could observe the (critical) slowing down of the relaxation dynamics close to the MBL transition and our results were now published in PRL (1D) and PRX (2D).

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 one dimension.

In our first recent work, now published in PRL, we experimentally and numerically investigate the regime close to the many-body localisation transition in 1D quasi-periodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behaviour near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an improved estimate of the transition point. 

In a second set of experiments, which recently appeared in PRX, we experimentally explore the equivalent dynamics in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. In this regime, where numerical simulations are not feasible, we again observe a dramatic slowing down of the relaxation for intermediate disorder strengths. Furthermore, beyond a critical disorder strength, we see negligible relaxation on experimentally accessible time scales, indicating a possible transition into a two-dimensional MBL phase.