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

AbstractFor 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 Δ we define ζ by Δ=cosζ, and put it in a region 0⩽ζ<π/2s of the gapless regime: −1<Δ⩽1 (0⩽ζ