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arXiv:1112.3310 · Journal of High Energy Physics

Classical tau-function for quantum spin chains

A. Alexandrov, Vladimir Kazakov, Sébastien Leurent, Zengo Tsuboi, Anton Vladimirovich Zabrodin

Published Sep 1, 2013• 60 citations
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Abstract

Abstract For an arbitrary generalized quantum integrable spin chain we introduce a “masterT-operator” which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show that the functional relations for the transfer matrices are equivalent to an infinite set of model-independent bilinear equations of the Hirota form for the masterT-operator, which allows one to identify it withτ-function of an integrable hierarchy of classical soliton equations. In this paper we consider spin chains with rationalGL(N)-invariantR-matrices but the result is independent of a particular functional form of the transfer matrices and directly applies to quantum integrable models with more general (trigonometric and elliptic)R-matrices and to supersymmetric spin chains.

DOI
10.1007/jhep09(2013)064

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