Third-neighbor correlators of a one-dimensional spin-1/2 Heisenberg antiferromagnet

We exactly evaluate the third-neighbor correlator <(SjSj+3z)-S-z> and all the possible nonzero correlators <(SjSj+1Sj+2Sj+3delta)-S-alpha-S-beta-S-gamma> of the one-dimensional spin-1/2 Heisenberg XXX antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln 2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.