The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914461893263360 |
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| author | Tasaki, Hal |
| author_facet | Tasaki, Hal |
| contents | Under the widely accepted but unproven assumption that the one-dimensional S=1 antiferromagnetic Heisenberg model has a unique gapped ground state, we prove that the model belongs to a nontrivial symmetry-protected topological (SPT) phase. In other words, we rigorously rule out the possibility that the model has a unique gapped ground state that is topologically trivial. To be precise, we assume that the models on open finite chains with boundary magnetic field have unique ground states with a uniform gap and prove that the ground state of the infinite chain has a nontrivial topological index. This further implies the presence of a gapless edge excitation in the model on the half-infinite chain and the existence of a topological phase transition in the model that interpolates between the Heisenberg chain and the trivial model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped Tasaki, Hal Statistical Mechanics Mathematical Physics Under the widely accepted but unproven assumption that the one-dimensional S=1 antiferromagnetic Heisenberg model has a unique gapped ground state, we prove that the model belongs to a nontrivial symmetry-protected topological (SPT) phase. In other words, we rigorously rule out the possibility that the model has a unique gapped ground state that is topologically trivial. To be precise, we assume that the models on open finite chains with boundary magnetic field have unique ground states with a uniform gap and prove that the ground state of the infinite chain has a nontrivial topological index. This further implies the presence of a gapless edge excitation in the model on the half-infinite chain and the existence of a topological phase transition in the model that interpolates between the Heisenberg chain and the trivial model. |
| title | The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2407.17041 |