Transition from ergodic to many-body localization regimes in open quantum systems in terms of the neural-network ansatz

The purpose of our work is to investigate asymptotic stationary states of an open disordered many-body quantum model which is characterized by an ergodic - many-body localization (MBL) phase transition. To find these states, we use the neural-network ansatz, a new method of modeling complex many-body quantum states discussed in the recent literature. Our main result is that that the ergodic phase - MBL transition is detectable in the performance of the neural network that is trained to reproduce the asymptotic states of the model. While the network is able to reproduce, with a relatively high accuracy, ergodic states, it fails to do so when the model system enter the MBL phase. We conclude that MBL features of the model translate into the cost function landscape which becomes corrugated and acquires many local minima.