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All regular $4 \times 4$ solutions of the Yang-Baxter equation

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arxiv 2306.10423 v3 pith:33GIKZZY submitted 2023-06-17 hep-th cond-mat.stat-mechmath-phmath.MPnlin.SI

Luke Corcoran , Marius de Leeuw This is my paper · ORCID
classification hep-thcond-mat.stat-mechmath-phmath.MPnlin.SI
keywords modelsequationregularsolutionstimesyang-baxterapartblock
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abstract

We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer matrices that have a non-trivial Jordan block structure. One model corresponds to a non-diagonalisable integrable deformation of the XXX spin chain.

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Cited by 3 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. All 4 x 4 solutions of the quantum Yang-Baxter equation

    math-ph 2024-11 unverdicted novelty 8.0 of 10

    The authors complete the classification of all 4×4 solutions of the quantum Yang-Baxter equation, including non-regular cases, and examine their relation to Lax operators.

  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.

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