Stacked tree construction for free-fermion projected entangled pair states
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912558053588992 |
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| author | He, Yuman Li, Kangle Zhang, Yanbai Po, Hoi Chun |
| author_facet | He, Yuman Li, Kangle Zhang, Yanbai Po, Hoi Chun |
| contents | The tensor network representation of a state in higher dimensions, say a projected entangled-pair state (PEPS), is typically obtained indirectly through variational optimization or imaginary-time Hamiltonian evolution. Here, we propose a divide-and-conquer approach to directly construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. Our approach relies on first obtaining a tree tensor network description of the state in local subregions. Next, a stacking procedure is used to combine the local trees into a PEPS. Lastly, the local tensors are compressed to obtain a more efficient description. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09377 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stacked tree construction for free-fermion projected entangled pair states He, Yuman Li, Kangle Zhang, Yanbai Po, Hoi Chun Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics The tensor network representation of a state in higher dimensions, say a projected entangled-pair state (PEPS), is typically obtained indirectly through variational optimization or imaginary-time Hamiltonian evolution. Here, we propose a divide-and-conquer approach to directly construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. Our approach relies on first obtaining a tree tensor network description of the state in local subregions. Next, a stacking procedure is used to combine the local trees into a PEPS. Lastly, the local tensors are compressed to obtain a more efficient description. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice. |
| title | Stacked tree construction for free-fermion projected entangled pair states |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2308.09377 |