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This paper constructs a novel three-parameter Yang-Baxter equation for the chiral Potts model, extending the unification of solvable edge and vertex models by treating the star-triangle relation as a fundamental ingredient rather than an alternative form. By incorporating an extra spectral parameter derived from the model's specific Hamiltonian structure, the work advances the mathematical framework for integrable systems and quantum Hamiltonians with nearest-neighbor interactions. The research primarily targets theoretical physicists and mathematicians working in statistical mechanics and high-energy theory rather than immediate applications in AI or quantum computing hardware.
The Yang-Baxter Equation for the Chiral Potts Model and Integrable Parafermions
arXiv:2606.11146v1 Announce Type: cross Abstract: A new type of Yang-Baxter equation (YBE) for $R$-matrices parameterized by three spectral parameters is constructed from the star-triangle and star-star relations for the chiral Potts model. As the $Z_N$ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for $N>2$, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. This combined with the fact that the quantum Hamiltonians of edge models like Ising contain both nearest neighbor interaction and onsite potential terms results in the extra spectral parameter of the $R$-operator. My construction extends the recent unification of solvable edge and vertex models which recasts Onsager's star-triangle relation from a mere alternative form of the YBE for edge models to its underlying ingredient.
Abstract:A new type of Yang-Baxter equation (YBE) for $R$-matrices parameterized by three spectral parameters is constructed from the star-triangle and star-star relations for the chiral Potts model. As the $Z_N$ symmetric generalization to the Ising model, its Boltzmann weights are known to depend on two variables describing a curve with genus larger than one for $N>2$, except for the self-dual point corresponding to the Fateev-Zamolodchikov chain. This combined with the fact that the quantum Hamiltonians of edge models like Ising contain both nearest neighbor interaction and onsite potential terms results in the extra spectral parameter of the $R$-operator. My construction extends the recent unification of solvable edge and vertex models which recasts Onsager's star-triangle relation from a mere alternative form of the YBE for edge models to its underlying ingredient.
Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2606.11146 [math-ph]
(or arXiv:2606.11146v1 [math-ph] for this version)
https://doi.org/10.48550/arXiv.2606.11146 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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