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

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.

36 pages + references

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• Lectures on Yangian Symmetry
• Algebraic Bethe Circuits
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• The Integrable (Hyper)eclectic Spin Chain
• Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations

Cited by in corpus (1)

• Almost local integrable models from supersymmetry algebras