Automatic structural optimization of tree tensor networks
The tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.013031 |
| _version_ | 1797210610206769152 |
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| author | Toshiya Hikihara Hiroshi Ueda Kouichi Okunishi Kenji Harada Tomotoshi Nishino |
| author_facet | Toshiya Hikihara Hiroshi Ueda Kouichi Okunishi Kenji Harada Tomotoshi Nishino |
| author_sort | Toshiya Hikihara |
| collection | DOAJ |
| description | The tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as the density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain, having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed. |
| first_indexed | 2024-04-24T10:13:20Z |
| format | Article |
| id | doaj.art-d6bdf3a69b1247b990b64f543042e241 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:20Z |
| publishDate | 2023-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-d6bdf3a69b1247b990b64f543042e2412024-04-12T17:27:45ZengAmerican Physical SocietyPhysical Review Research2643-15642023-01-015101303110.1103/PhysRevResearch.5.013031Automatic structural optimization of tree tensor networksToshiya HikiharaHiroshi UedaKouichi OkunishiKenji HaradaTomotoshi NishinoThe tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as the density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain, having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.http://doi.org/10.1103/PhysRevResearch.5.013031 |
| spellingShingle | Toshiya Hikihara Hiroshi Ueda Kouichi Okunishi Kenji Harada Tomotoshi Nishino Automatic structural optimization of tree tensor networks Physical Review Research |
| title | Automatic structural optimization of tree tensor networks |
| title_full | Automatic structural optimization of tree tensor networks |
| title_fullStr | Automatic structural optimization of tree tensor networks |
| title_full_unstemmed | Automatic structural optimization of tree tensor networks |
| title_short | Automatic structural optimization of tree tensor networks |
| title_sort | automatic structural optimization of tree tensor networks |
| url | http://doi.org/10.1103/PhysRevResearch.5.013031 |
| work_keys_str_mv | AT toshiyahikihara automaticstructuraloptimizationoftreetensornetworks AT hiroshiueda automaticstructuraloptimizationoftreetensornetworks AT kouichiokunishi automaticstructuraloptimizationoftreetensornetworks AT kenjiharada automaticstructuraloptimizationoftreetensornetworks AT tomotoshinishino automaticstructuraloptimizationoftreetensornetworks |