Nuclear norm regularized loop optimization for tensor network
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929577963552768 |
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| author | Homma, Kenji Okubo, Tsuyoshi Kawashima, Naoki |
| author_facet | Homma, Kenji Okubo, Tsuyoshi Kawashima, Naoki |
| contents | We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical 2D Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nuclear norm regularized loop optimization for tensor network Homma, Kenji Okubo, Tsuyoshi Kawashima, Naoki Statistical Mechanics We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical 2D Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion. |
| title | Nuclear norm regularized loop optimization for tensor network |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2306.17479 |