Physics-informed neural network model for quantum impurity problems based on Lehmann representation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909407645794304 |
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| author | Kakizawa, Fumiya Terasaki, Satoshi Shinaoka, Hiroshi |
| author_facet | Kakizawa, Fumiya Terasaki, Satoshi Shinaoka, Hiroshi |
| contents | We propose a physics-informed neural network (PINN) model to efficiently predict the self-energy of Anderson impurity models (AIMs) based on the Lehmann representation. As an example, we apply the PINN model to a single-orbital AIM (SAIM) for a noninteracting electron bath with a semicircular density of states. Trained across a wide range of onsite Coulomb interactions $U$ and hybridization strengths $V$, the PINN model demonstrates high accuracy in both $U$-$V$ and Matsubara-frequency spaces. Additionally, we investigate the effectiveness of physical constraints implemented in the PINN model. For example, We show that the Lehmann representation allows the PINN model to reduce the maximum test error in an electron filling by a factor of approximately 7.8. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physics-informed neural network model for quantum impurity problems based on Lehmann representation Kakizawa, Fumiya Terasaki, Satoshi Shinaoka, Hiroshi Strongly Correlated Electrons We propose a physics-informed neural network (PINN) model to efficiently predict the self-energy of Anderson impurity models (AIMs) based on the Lehmann representation. As an example, we apply the PINN model to a single-orbital AIM (SAIM) for a noninteracting electron bath with a semicircular density of states. Trained across a wide range of onsite Coulomb interactions $U$ and hybridization strengths $V$, the PINN model demonstrates high accuracy in both $U$-$V$ and Matsubara-frequency spaces. Additionally, we investigate the effectiveness of physical constraints implemented in the PINN model. For example, We show that the Lehmann representation allows the PINN model to reduce the maximum test error in an electron filling by a factor of approximately 7.8. |
| title | Physics-informed neural network model for quantum impurity problems based on Lehmann representation |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.18835 |