Classifying integrable spin-1/2 chains with nearest neighbour interactions

Marius de Leeuw; Anton Pribytok; Paul Ryan

doi:10.1088/1751-8121/ab529f

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arXiv · 1904.12005

Classifying integrable spin-1/2 chains with nearest neighbour interactions

Marius de Leeuw·Anton Pribytok·Paul Ryan

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Abstract

We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and reduces to the permutation operator at some particular point. We find a total of 14 independent solutions, 8 of which correspond to well-known eight or lower vertex models. The remaining 6 models appear to be new and some have peculiar properties such as not being diagonalizable or being nilpotent. Furthermore, for even R-matrices, we find a bijection between solutions of the Yang-Baxter equation and the graded Yang-Baxter equation which extends our results to the graded two-dimensional case.

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Marius de Leeuw, Anton Pribytok, Paul Ryan. 2020-03-23. Classifying integrable spin-1/2 chains with nearest neighbour interactions. https://doi.org/10.1088/1751-8121%2Fab529f

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