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arXiv · 2503.08109

Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation

Somnath Maity·Pramod Padmanabhan·Vladimir Korepin
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Abstract

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.

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Somnath Maity, Pramod Padmanabhan, Vladimir Korepin. 2025-03-11. Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation. https://doi.org/10.1007/jhep05(2025)206

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