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Hidden quantum R-matrix in discrete time classical Heisenberg magnet

A. Zabrodin
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Abstract

We construct local M-operators for an integrable discrete time version of the classical Heisenberg magnet by convolution of the twisted quantum trigonometric 4$\times$4 R-matrix with certain vectors in its "quantum" space. Components of the vectors are identified with $τ$-functions of the model. Hirota's bilinear formalism is extensively used. The construction generalizes the known representation of M-operators in continuous time models in terms of Lax operators and classical $r$-matrix.

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BibTeXRIS

A. Zabrodin. 1998-01-22. Hidden quantum R-matrix in discrete time classical Heisenberg magnet. https://arxiv.org/abs/solv-int/9710015

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