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

Fuente: arXiv
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Autor principal: Chen, Anffany
Formato: Preprint
Publicado: 2023
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author Chen, Anffany
author_facet Chen, Anffany
contents We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered 1D and 2D lattices. We perform supervised training of convolutional neural networks (CNNs) using labelled many-body wavefunctions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the disorder-averaged 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 $W_c\sim2.8$ 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 wavefunctions while rendering delocalized wavefunctions nearly featureless.
format Preprint
id arxiv_https___arxiv_org_abs_2312_09223
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
Chen, Anffany
Disordered Systems and Neural Networks
Mesoscale and Nanoscale Physics
Statistical Mechanics
Strongly Correlated Electrons
We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered 1D and 2D lattices. We perform supervised training of convolutional neural networks (CNNs) using labelled many-body wavefunctions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the disorder-averaged 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 $W_c\sim2.8$ 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 wavefunctions while rendering delocalized wavefunctions nearly featureless.
title Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
topic Disordered Systems and Neural Networks
Mesoscale and Nanoscale Physics
Statistical Mechanics
Strongly Correlated Electrons
url https://arxiv.org/abs/2312.09223