The product structure of MPS-under-permutations
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913016830754816 |
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| author | Florido-Llinàs, Marta Alhambra, Álvaro M. Trivedi, Rahul Schuch, Norbert Pérez-García, David Cirac, J. Ignacio |
| author_facet | Florido-Llinàs, Marta Alhambra, Álvaro M. Trivedi, Rahul Schuch, Norbert Pérez-García, David Cirac, J. Ignacio |
| contents | Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ansätze simpler than tensor networks in systems whose structure is invariant under permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The product structure of MPS-under-permutations Florido-Llinàs, Marta Alhambra, Álvaro M. Trivedi, Rahul Schuch, Norbert Pérez-García, David Cirac, J. Ignacio Quantum Physics Strongly Correlated Electrons Mathematical Physics Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ansätze simpler than tensor networks in systems whose structure is invariant under permutations. |
| title | The product structure of MPS-under-permutations |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2410.19541 |