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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 056, 41 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.056
(Mi sigma614)
 

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

Tetsuo Deguchi, Jun Sato

Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
References:
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.
Keywords: quantum group; integrable higher-spin XXZ chain; correlation function; multiple integral; fusion method; Bethe ansatz; one-point function.
Received: October 29, 2010; in final form May 26, 2011; Published online June 10, 2011
Bibliographic databases:
Document Type: Article
MSC: 82B23
Language: English
Citation: Tetsuo Deguchi, Jun Sato, “Quantum Group $U_q(sl(2))$ Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain”, SIGMA, 7 (2011), 056, 41 pp.
Citation in format AMSBIB
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\by Tetsuo Deguchi, Jun Sato
\paper Quantum Group $U_q(sl(2))$ Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain
\jour SIGMA
\yr 2011
\vol 7
\papernumber 056
\totalpages 41
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