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

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arxiv 1904.12005 v3 pith:MRMGK3S5 submitted 2019-04-26 math-ph cond-mat.stat-mechhep-thmath.MPnlin.SI

Marius de Leeuw , Anton Pribytok , Paul Ryan This is my paper · ORCID
classification math-phcond-mat.stat-mechhep-thmath.MPnlin.SI
keywords integrablechainsequationfindformgradedmodelsr-matrices
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Simple Necessary and Sufficient Condition for Yang--Baxter Integrability

    cond-mat.stat-mech 2026-07 conditional novelty 8.0 of 10

    The Reshetikhin condition on a nearest-neighbour spin-chain Hamiltonian is sufficient (and necessary) for the existence of a regular difference-form Yang–Baxter R-matrix, resolving a 1980s conjecture.

  2. Long-range to the Rescue of Yang-Baxter II

    hep-th 2025-07 conditional novelty 6.0 of 10

    A long-range Bethe ansatz produces four-magnon eigenstates, recursively built from three-magnon data, for the one-loop spin chain of a marginally deformed Z2 orbifold of N=4 SYM.

  3. An integrable deformed Landau-Lifshitz model with particle production?

    hep-th 2025-06 conditional novelty 6.0 of 10

    The Class 5 spin chain's continuum limit is a non-unitary deformed Landau-Lifshitz model with a conserved-charge tower and a soft 1-to-2 S-matrix.

  4. Fifteen-vertex models with non-symmetric $R$ matrices

    nlin.SI 2019-08 conditional novelty 6.0 of 10

    Four families of non-symmetric R matrices and three families of K matrices solve the Yang-Baxter equations for regular fifteen-vertex ice-rule models.

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