Machine learning many-body quantum phases in non-equilibrium systems with single-particle mobility edge

The many-body quantum phases in isolated quasi-periodic systems are an intriguing subject that cannot be described by the framework of equilibrium statistical mechanics. One main challenge lies in the fact that there are no well-established order parameters that can definitively determine the number and nature of possible dynamical phases. In particular, a non-ergodic metallic phase has been proposed as a novel phase between the many-body localized and thermalized phases in the Generalized Aubry Andre model, a one-dimensional quasiperiodic chain with single-particle mobility edge (SPME). While the existence and origin of the non-ergodic metal remain elusive, this phase has been conjectured as a natural consequence of the presence of SPME. In this talk, I will present a general machine-learning protocol that can determine the phase diagrams of systems with controversial phases, a situation where the conventional supervised learning is not applicable. By applying our neural-network based method to study multiple different models with SPME, I will discuss the stability of the non-ergodic metal and whether it originates from SPME.