Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917998010302464 |
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| author | Sommer, Ophelia Evelyn Wen, Xueda Vishwanath, Ashvin |
| author_facet | Sommer, Ophelia Evelyn Wen, Xueda Vishwanath, Ashvin |
| contents | Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC for extended $d = 1$ systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states (MPS), and show that for translationally invariant MPS this gives rise to a quantized invariant. We demonstrate our approach with an exactly solvable model and numerical calculations for generic models using iDMRG |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States Sommer, Ophelia Evelyn Wen, Xueda Vishwanath, Ashvin Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC for extended $d = 1$ systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states (MPS), and show that for translationally invariant MPS this gives rise to a quantized invariant. We demonstrate our approach with an exactly solvable model and numerical calculations for generic models using iDMRG |
| title | Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.05316 |