A Neural Network approach to the Many Body Localized Phase

The Many Body Localized Phase (MBL) is a phase that exists in distinction to the Ergodic phase. As such, the MBL phase violates the Eigenstate Thermalization Hypothesis and does not undergo thermalization. In this paper, the Ergodic to MBL phase transition will be explored with Artificial Neural Networks (ANNs) trained on a Heisenberg spin chain with disorder. One of the main aspects explored in this article is if neural networks can in fact be trained to perceive a difference in both of these phases, and moreover, examine the as-of-now unanswered question of whether or not information about the MBL phase is encoded in the many-body density matrix at infinite temperature req(T !•). A phase diagram is generated, along with probability curves that predict MBL given a level of disorder. Finally, reverse engineering is done to understand the ANN and evidence is found that the ANN is learning about the entanglement entropy.