LAUSR

Many-body localization is a striking mechanism that prevents interacting quantum systems from thermalizing. The absence of thermalization behaviour manifests itself, for example, in a remanence of local particle number configurations, a quantity that is robust over a parameter range -- unlike the situation in other instances of integrability. Local particle numbers are directly accessible in state-of-the-art quantum simulators, in systems of cold atoms even in two spatial dimensions. Yet, the classical simulation to benchmark such quantum simulators is highly challenging. In this work, we present a comprehensive tensor network simulation of a many-body localized systems in spatial dimensions using a variant of an iPEPS algorithm. The required translational invariance can be restored by implementing the disorder into an auxiliary spin system, providing an exact disorder average under dynamics. We observe signatures of many-body localization for the infinite system. Interestingly, in this setting of finitely many disorder values, localization emerges in the interacting regime, for which we provide an intuitive argument, while Anderson localization is absent. We benchmark our results against a simulation involving non-interacting fermions and find results compatible with an absence of localization.