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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.11172 |
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| _version_ | 1866917333455339520 |
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| author | Zhang, Zhao |
| author_facet | Zhang, Zhao |
| contents | Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's decorated star-triangle relation by the $R$-matrix, which is more general than the previous `free-fermion algebra' by Maassarani and more special than free fermions as in the context of exactly solvable quantum models or integrable classical two-dimensional vertex models dual to quantum spin chains. Free fermionic $R$-matrices are of the difference form and have a conjugation symmetry. These free Hamiltonians may sometimes be deformed by the conjugation operator to describe an integrable interacting system with non-relativistic $R$-matrices, as are the cases of the Hubbard model and the XY model in a longitudinal field. A further criterion is obtain on precisely when such deformations remain integrable. A practical procedure is proposed to iteratively solve the free fermionic $R$-matrices from local Hamiltonians, which can be used to construct non-relativistic $R$-matrices if the conditions are met. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrable Free and Interacting Fermions Zhang, Zhao Exactly Solvable and Integrable Systems Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's decorated star-triangle relation by the $R$-matrix, which is more general than the previous `free-fermion algebra' by Maassarani and more special than free fermions as in the context of exactly solvable quantum models or integrable classical two-dimensional vertex models dual to quantum spin chains. Free fermionic $R$-matrices are of the difference form and have a conjugation symmetry. These free Hamiltonians may sometimes be deformed by the conjugation operator to describe an integrable interacting system with non-relativistic $R$-matrices, as are the cases of the Hubbard model and the XY model in a longitudinal field. A further criterion is obtain on precisely when such deformations remain integrable. A practical procedure is proposed to iteratively solve the free fermionic $R$-matrices from local Hamiltonians, which can be used to construct non-relativistic $R$-matrices if the conditions are met. |
| title | Integrable Free and Interacting Fermions |
| topic | Exactly Solvable and Integrable Systems Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2603.11172 |