Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911523694182400 |
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| author | Liu, Xi Zhao, Yujun Wan, Chun Yu Zhang, Yang Liu, Junwei |
| author_facet | Liu, Xi Zhao, Yujun Wan, Chun Yu Zhang, Yang Liu, Junwei |
| contents | We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical 3-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: trained on $10 \times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training -- and the accuracy improves with system size, with a computational time speed-up of $10^{3}$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_17665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems Liu, Xi Zhao, Yujun Wan, Chun Yu Zhang, Yang Liu, Junwei Computational Physics Strongly Correlated Electrons Artificial Intelligence Quantum Physics We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical 3-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: trained on $10 \times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training -- and the accuracy improves with system size, with a computational time speed-up of $10^{3}$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply. |
| title | Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems |
| topic | Computational Physics Strongly Correlated Electrons Artificial Intelligence Quantum Physics |
| url | https://arxiv.org/abs/2502.17665 |