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Abstract

We study the high-energy phase diagram of a two-dimensional spin 1/2 Heisenberg model on a square lattice in the presence of either quenched or quasiperiodic disorder. The use of large-scale tensor network numerics allows us to compute the bipartite entanglement entropy for systems of up to 60×7 lattice sites. We provide evidence for the existence of a many-body localized regime for large disorder strength that features an area law in excited states and that violates the eigenstate thermalization hypothesis. From a finite-size analysis, we determine an estimate for the critical disorder strength where the transition to the ergodic regime occurs in the quenched case.