Signatures of the Many-Body Localized Regime in Two Dimensions*

Lessons from Anderson localization highlight the importance of dimensionality of real space for
localization due to disorder. More recently, studies of many-body localization have focussed on
the phenomenon in one dimension using techniques of exact diagonalization and tensor networks.
On the other hand, experiments in two dimensions have provided concrete results going beyond
the previously numerically accessible limits while posing several challenging questions. We present
the first large-scale numerical examination of a disordered Bose-Hubbard model in two dimensions
realized in cold atoms, which shows entanglement based signatures of many-body localization. By
generalizing a low-depth quantum circuit to two dimensions we approximate eigenstates in the ex-
perimental parameter regimes for large systems, which is beyond the scope of exact diagonalization.
A careful analysis of the eigenstate entanglement structure provides an indication of the putative
phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range
consistent with experiments.