Correlation amplitude for theS=12XXZspin chain in the critical region: Numerical renormalization-group study of an open chain

The density-matrix renormalization-group technique is used to calculate the spin-correlation functions $〈S_j^x{S}_k^x〉$ and $〈S_j^z{S}_k^z〉$ of the one-dimensional $S=\frac{1}{2}$ $\mathrm{XXZ}$ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.