Pure gapped ground states of spin chains are short-range entangled
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909911429939200 |
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| author | De Roeck, Wojciech Fraas, Martin Carvalho, Bruno de O. |
| author_facet | De Roeck, Wojciech Fraas, Martin Carvalho, Bruno de O. |
| contents | We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pure gapped ground states of spin chains are short-range entangled De Roeck, Wojciech Fraas, Martin Carvalho, Bruno de O. Mathematical Physics Quantum Physics We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk. |
| title | Pure gapped ground states of spin chains are short-range entangled |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.14699 |