Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912878370488320 |
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| author | Xu, Xiaotian Wen, Wuxiao Yang, Tao Zhang, Xin Cao, Junpeng |
| author_facet | Xu, Xiaotian Wen, Wuxiao Yang, Tao Zhang, Xin Cao, Junpeng |
| contents | In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra Xu, Xiaotian Wen, Wuxiao Yang, Tao Zhang, Xin Cao, Junpeng Mathematical Physics In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed. |
| title | Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2510.27312 |