The discovery of many-body localization (MBL) in interacting quantum systems, because of its wide implication for fundamental concepts such as thermalization in isolated quantum systems, has given rise to extensive research in the intervening decade and a half. However, its study is complicated both on the analytical front as well as numerical, though definite progress is being made. It seems to be clear that MBL exists in one-dimensional spin models, as first suggested by numerical simulations. Obtaining results in higher dimensions with the same amount of rigor appears distant at present, though studies have shown that a proper treatment of rare fluctuations is crucial for answering this issue.
On the numerical front, models in higher dimensions as well as fully interacting fermionic models suffer the problem of the explosion of the Hilbert space with size. Consequently, we recently explored the possibility of MBL in a system of two-dimensional electrons (interacting via a Coulomb interaction) in the presence of disorder, when placed in a large perpendicular magnetic field in the extreme quantum (lowest Landau level) limit. While this situation is significantly more challenging than one-dimensional spin models, we are able to consider both lattice and continuum models; the latter bypass commensurability requirements imposed by lattices in higher dimensions. Using eigenvalue statistics as well as time evolution methods to study several different cases, we find that MBL is very strongly affected by topology, even more so than earlier analytic arguments suggest.