Higher Berry Connection for Matrix Product States
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916239436152832 |
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| author | Ohyama, Shuhei Ryu, Shinsei |
| author_facet | Ohyama, Shuhei Ryu, Shinsei |
| contents | In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase -- a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wavefunction overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized Matrix Product States (MPS) over a parameter space. We demonstrate the use of our formula for simple non-trivial models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Berry Connection for Matrix Product States Ohyama, Shuhei Ryu, Shinsei Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase -- a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wavefunction overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized Matrix Product States (MPS) over a parameter space. We demonstrate the use of our formula for simple non-trivial models. |
| title | Higher Berry Connection for Matrix Product States |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2405.05327 |