Unitary long-time evolution with quantum renormalization groups and artificial neural networks

In this work we combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute the long-time coherent dynamics of large, many-body localized systems in non-perturbative regimes including the effects of many-body resonances. Concretely, we use this approach to describe the spatiotemporal buildup of many-body localized spin glass order in random Ising chains. We observe a fundamental difference to a non-interacting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to strongly disordered two-dimensional Ising models highlighting that our method can be used also for the description of the real-time dynamics of nonergodic quantum matter in a general context.