Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911895107141632 |
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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 |