Exploiting the Hermitian symmetry in tensor network algorithms
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912201784164352 |
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| author | van Alphen, Oscar Kleijweg, Stijn V. Hasik, Juraj Corboz, Philippe |
| author_facet | van Alphen, Oscar Kleijweg, Stijn V. Hasik, Juraj Corboz, Philippe |
| contents | Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods based on projected entangled-pair states (PEPS). For real-valued tensors the Hermitian symmetry defines a $\mathbb{Z}_2$ symmetry on the combined bra and ket auxiliary level of the tensors. By implementing this symmetry, a speedup of the computation time by up to a factor 4 can be achieved, while expectation values of observables and reduced density matrices remain Hermitian by construction. Benchmark results based on the corner transfer matrix renormalization group (CTMRG) and higher-order tensor renormalization group (HOTRG) are presented. We also discuss how to implement the Hermitian symmetry in the complex case, where a similar speedup can be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploiting the Hermitian symmetry in tensor network algorithms van Alphen, Oscar Kleijweg, Stijn V. Hasik, Juraj Corboz, Philippe Strongly Correlated Electrons Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods based on projected entangled-pair states (PEPS). For real-valued tensors the Hermitian symmetry defines a $\mathbb{Z}_2$ symmetry on the combined bra and ket auxiliary level of the tensors. By implementing this symmetry, a speedup of the computation time by up to a factor 4 can be achieved, while expectation values of observables and reduced density matrices remain Hermitian by construction. Benchmark results based on the corner transfer matrix renormalization group (CTMRG) and higher-order tensor renormalization group (HOTRG) are presented. We also discuss how to implement the Hermitian symmetry in the complex case, where a similar speedup can be achieved. |
| title | Exploiting the Hermitian symmetry in tensor network algorithms |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.11596 |