Quantum inverse scattering for the 20-vertex model up to Dynkin automorphism: 3D Poisson structure, triangular height functions, weak integrability

2024/07/12 by Pete Rigas, Rigas, Pete
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2407.11066

Abstract

We initiate a novel application of the quantum inverse scattering method for the 20-vertex model, building upon seminal work from Faddeev and Takhtajan on the study of Hamiltonian systems. In comparison to a previous work of the author in late 2023 which characterized integrability of a Hamiltonian flow for the 6-vertex model from integrability of inhomogeneous limit shapes, formalized in a work of Keating, Reshetikhin and Sridhar, notions similar to those of integrability can be realized for the 20-vertex model by studying new classes of higher-dimensional L-operators. Such L-operators provided by Boos and colleagues have algebraic, combinatorial, and geometric, qualities, all of which impact leading order approximations of correlations, products of L-operators, the transfer matrix, and the quantum monodromy matrix.

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