Numerical evidence for a many-body localization transition in two dimensions*

We use the stochastic series expansion quantum Monte Carlo method, together with the eigenstate-to-Hamiltonian mapping approach, to probe the many-body localization transition in the two dimensional spin-half Heisenberg model with magnetic disorder. We establish the localised nature of the ground state by studying the spin stiffness, local entanglement entropy, and local magnetization. By mapping the ground state of this parent Hamiltonian to excited states of target Hamiltonians, we determine the many-body localized regime in an energy-resolved phase diagram. Our study presents concrete numerical evidence for the existence of a many-body localized phase in two dimensions.