We present accurate numerical estimates for the correlation amplitudes of leading and main subleading terms of the two- and four-spin correlation functions in the one-dimensional spin-$1/2$ $\mathrm{XXZ}$ model under a magnetic field. These data are obtained by fitting the correlation functions, computed numerically with the density-matrix renormalization-group method, to the corresponding correlation functions in the low-energy effective theory. For this purpose we have developed the Abelian bosonization approach to the spin chain under the open-boundary conditions. We use the numerical data of the correlation amplitudes to quantitatively estimate spin gaps induced by a transverse staggered field and by exchange anisotropy.

• Received 17 October 2003

DOI:https://doi.org/10.1103/PhysRevB.69.064427