Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 056, 41 pages      arXiv:1105.4952      https://doi.org/10.3842/SIGMA.2011.056
Contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”

Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain

Tetsuo Deguchi and Jun Sato
Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan

Received October 29, 2010, in final form May 26, 2011; Published online June 10, 2011

Abstract
We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.

Key words: quantum group; integrable higher-spin XXZ chain; correlation function; multiple integral; fusion method; Bethe ansatz; one-point function.

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