Many-body mobility edges in one and two dimensions revealed by convolutional neural networks

We adapt a machine -learning approach to study the many -body localization transition in interacting fermionic systems on disordered one-dimensional (1D) and two-dimensional (2D) lattices. We perform supervised training of convolutional neural networks (CNNs) using labeled many -body wave functions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the disorderaveraged predictions of the CNNs to generate energy -resolved phase diagrams, which exhibit many -body mobility edges. We provide finite -size estimates of the critical disorder strengths at Bic - 2.8 and 9.8 for 1D and 2D systems of 16 sites, respectively. Our results agree with the analysis of energy -level statistics and inverse participation ratio. By examining the convolutional layer, we unveil its feature extraction mechanism which highlights the pronounced peaks in localized many -body wave functions while rendering delocalized wave functions nearly featureless.