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Modern Physics Letters A

INTEGRABLE MULTIPARAMETRIC SU (N) CHAIN

Angela Foerster, I. Roditi, Ligia M. C. S. Rodrigues

Published Apr 20, 1996• 7 citations
Publisher

Abstract

We analyze integrable models associated to a multiparametric SU (N)R-matrix. We show that the Hamiltonians describe SU (N) chains with twisted boundary conditions and that the underlying algebraic structure is the multiparametric deformation of SU (N) enlarged by the introduction of a central element.
DOI
10.1142/s0217732396001016

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Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting charges, the underlying quantum group structures had not yet been recognised. In this paper, we provide a quantum group-theoretical description for the family of long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains up to first order in the deformation parameter. In particular, we show that the deformations are obtained via a twist of the algebraic structure of the underlying quantum group. This twisting results in a generally non-associative algebra that has a non-trivial Drinfeld associator. The Drinfeld associator is then shown to encode the information about the long-range interaction terms for the integrable spin chain. Moreover, the deformed quantum group is shown to contain a large perturbatively associative substructure, thus ensuring the perturbative integrability of the long-range model. The deformed quantum group provides explicit expressions for the Lax operators and R-matrices of the long-range deformed models, which manifestly satisfy the RLL relation and the Yang-Baxter equation up to first order in the deformation parameter. In order to derive the results, we introduce algebra elements that we call the algebraic charge densities. As a side result, we provide a conjecture for the explicit expressions of the undeformed charge densities in terms of these algebra elements.