Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Maity, Somnath Padmanabhan, Pramod Korepin, Vladimir |
| author_facet | Maity, Somnath Padmanabhan, Pramod Korepin, Vladimir |
| contents | We construct invertible spectral parameter dependent Yang-Baxter solutions ($R$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using supersymmetry (SUSY) algebras. The resulting $R$-matrices are regular leading to local non-hermitian Hamiltonians written in terms of the SUSY generators. As particular examples we Baxterize the $4\times 4$ constant non-invertible solutions of Hietarinta leading to nearest-neighbor Hamiltonians. On comparing with the literature we find two of the models are new. Apart from being non-hermitian, many of them are also non-diagonalizable with interesting spectrums. With appropriate representations of the SUSY generators we obtain spin chains in all local Hilbert space dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation Maity, Somnath Padmanabhan, Pramod Korepin, Vladimir High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems We construct invertible spectral parameter dependent Yang-Baxter solutions ($R$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using supersymmetry (SUSY) algebras. The resulting $R$-matrices are regular leading to local non-hermitian Hamiltonians written in terms of the SUSY generators. As particular examples we Baxterize the $4\times 4$ constant non-invertible solutions of Hietarinta leading to nearest-neighbor Hamiltonians. On comparing with the literature we find two of the models are new. Apart from being non-hermitian, many of them are also non-diagonalizable with interesting spectrums. With appropriate representations of the SUSY generators we obtain spin chains in all local Hilbert space dimensions. |
| title | Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.08109 |