Monte Carlo simulation of the S=(1/2 antiferromagnetic Heisenberg chain and the long-distance behavior of the spin-correlation function

We present a new Monte Carlo simulation of the correlation function C(r) between two spins separated by a distance r in the ground state of the spin-1/2 Heisenberg chain. The calculation is based on the Sutherland mapping between the spin-chain ground state and the six-vertex model at its critical temperature. New results are obtained for rings with the number of spins N=32 and 40. We give evidence that the asymptotic decay of C(r) at large r is slower than the 1/r behavior of Luther and Peschel, and that this might be attributed to a logarithmic factor, i.e., C(r)∼(A/r)(lnr/$r_0$ ${)}^{\sigma }$, with σ≊0.2 to 0.3.