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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.00782 |
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| _version_ | 1866913489151328256 |
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| author | Martyn, John M. Najafi, Khadijeh Luo, Di |
| author_facet | Martyn, John M. Najafi, Khadijeh Luo, Di |
| contents | Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00782 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Variational Neural-Network Ansatz for Continuum Quantum Field Theory Martyn, John M. Najafi, Khadijeh Luo, Di Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Lattice Computational Physics Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories. |
| title | Variational Neural-Network Ansatz for Continuum Quantum Field Theory |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Lattice Computational Physics |
| url | https://arxiv.org/abs/2212.00782 |