Emptiness formation probability 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 show an explicit formula for the multiple-integral representations of the emptiness formation probability (EFP) in the massless ground-state at zero temperature. We first derive it for the inhomogeneous spin-s XXZ chain, and then for the homogeneous chain, sending the spin-s inhomogeneous parameters to zero. 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 ∆ we define ζ by ∆ = cos ζ, and put it in a region 0 ≤ ζ < π/2s of the gapless regime: −1 < ∆ ≤ 1 (0 ≤ ζ < π), where ∆ = 1 (ζ = 0) corresponds to the antiferromagnetic point. We show explicitly in the region that the diagonal elements of the spin-s Gaudin matrix are expressed in terms of the density of the 2s-strings. We can also derive the EFP of the spin-s XXX chain from that of the spin-s XXZ chain through the XXX limit of sending ζ to zero. We calculate the correlation functions by the algebraic Bethe ansatz, taking advantage of the fusion construction of the R-matrix of the higher-spin representations of the affine quantum group. e-mail [email protected] e-mail [email protected] 1