Many-body mobility edges in 1D and 2D revealed by convolutional neural networks

Anffany Chen
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)
2023-12-14 00:00:00
We investigate the many-body localization transition in strongly correlated fermionic systems on disordered 1D and 2D lattices using convolutional neural networks (CNNs). Our approach involves supervised training of CNNs with labelled many-body wavefunctions at the infinitesimal and strong disorder limits. These trained CNNs, when applied to wavefunctions near the transition region, facilitate the construction of energy-resolved phase diagrams which reveal many-body mobility edges in both 1D and 2D systems. We provide finite-size estimates of critical disorder strengths at $W_c\sim2.8$ for 1D and $W_c\sim9.8$ for 2D systems. Our results agree the analyses of energy level statistics and inverse participation ratio. By examining the CNN's convolutional layer, we unveil its feature extraction mechanism which effectively highlights the pronounced peaks in the localized many-body wavefunctions.
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