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 time scales 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.