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| VOLUME 115 (2022) | ISSUE 12 | PAGE 809 |
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Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
K. Atalikov+*, A. Zotov+× 1)
+Steklov Mathematical Institute of Russian Academy of Sciences, 119991 Moscow, Russia * Institute for Theoretical and Experimental Physics of National Research Centre "Kurchatov Institute", 117218 Moscow, Russia ×National Research University Higher School of Economics, 119048 Moscow, Russia
Abstract
We propose a construction of 1+1 integrable Heisenberg-Landau-Lifshitz type equations in the glN case. The dynamical variables are matrix elements of N× N matrix S with the property S2= const• S. The Lax pair with spectral parameter is constructed by means of a quantum R-matrix satisfying the associative Yang-Baxter equation. Equations of motion for glN Landau-Lifshitz model are derived from the Zakharov-Shabat equations. The model is simplified when rank(S)=1. In this case the Hamiltonian description is suggested. The described family of models includes the elliptic model coming from GLN Baxter-Belavin elliptic R-matrix. In N=2 case the widely known Sklyanin's elliptic Lax pair for XYZ Landau-Lifshitz equation is reproduced. Our construction is also valid for trigonometric and rational degenerations of the elliptic R-matrix. |