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

• Main Authors: Tetsuo Deguchi, Jun Sato
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2011-06-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: quantum group; integrable higher-spin XXZ chain; correlation function; multiple integral; fusion method; Bethe ansatz; one-point function
• Online Access: http://dx.doi.org/10.3842/SIGMA.2011.056

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.