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 nonperturbative 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 noninteracting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to strongly disordered twodimensional 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.

Automated summary

By combining quantum renormalization group approaches with deep artificial neural networks, we accurately describe the real-time evolution in strongly disordered quantum matter, including the effects of many-body resonances. Our method allows for the precise computation of long-time coherent dynamics in many-body localized systems, shedding light on the development of spin-glass order in random Ising chains. Furthermore, this approach can be applied to two-dimensional Ising models with strong disorder, demonstrating its potential for describing the real-time dynamics of nonergodic quantum matter in a general context.