Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method

For the integrable higher-spin XXX and XXZ spin chains we present multiple-integral representations for the correlation function of an arbitrary product of Hermitian elementary matrices in the massless ground state. We give a formula expressing it by a single term of multiple integrals. In particular, we explicitly derive the emptiness formation probability (EFP). We assume 2s-strings for the ground-state solution of the Bethe-ansatz equations for the spin-s XXZ chain, and solve the integral equations for the spin-s Gaudin matrix. In terms of the XXZ coupling A we define zeta by Delta = cos zeta, and put it in a region 0 <= zeta < pi/2s of the gapless regime: -1 < Delta <= 1 (0 <= zeta < pi), where Delta = (zeta = 0) corresponds to the antiferromagnetic point. We calculate the zero-temperature correlation functions by the algebraic Bethe-ansatz, introducing the Hermitian elementary matrices in the massless regime, and taking advantage of the fusion construction of the R-matrix of the higher-spin representations of the affine quantum group. (C) 2009 Elsevier B.V. All rights reserved.