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Hidden quantumR-matrix in the discrete-time classical Heisenberg magnet

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Abstract

We construct local M-operators for an integrable discrete-time version of the classical Heisenberg magnet by convoluting the twisted quantum trigonometric 4×4 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 the classical τ-matrix.

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Authors and Affiliations

  1. Joint Institute for Chemical Physics, Moscow, Russia

    A. V. Zabrodin

  2. Institute for Theoretical and Experimental Physics, Moscow, Russia

    A. V. Zabrodin

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  1. A. V. Zabrodin
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This paper was written at the request of the Editorial Board.

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 179–204, November, 2000.

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Zabrodin, A.V. Hidden quantumR-matrix in the discrete-time classical Heisenberg magnet. Theor Math Phys 125, 1455–1475 (2000). https://doi.org/10.1007/BF02551007

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  • DOI: https://doi.org/10.1007/BF02551007

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