Slow Many-Body Delocalization beyond One Dimension

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and timescales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder W-c(L, d) as a function of length L and width d. In the quasi-1D case W-c has a finite large-L limit at fixed d, which increases strongly with d. In the 2D case W-c(L, L) grows with L. The results are consistent with the avalanche picture of the many-body localization transition.