  We study the ground-state spin correlations in the gapless incommensurate
regime of a S=1/2 XXZ chain and a two-leg antiferromagnetic ladder under a
magnetic field, in which the gapless excitations form a Tomonaga-Luttinger (TL)
liquid. We calculate numerically the two-spin correlation functions and the
local magnetization in the two models using the density-matrix
renormalization-group method. By fitting the numerical results for an open XXZ
chain of 100 spins to correlation functions of a Gaussian model, we determine
the TL-liquid parameter K and the amplitudes of the correlation functions. The
value of K estimated from the fits is in excellent agreement with the exact
value obtained from the Bethe ansatz. We apply the same method to the open
ladder consisting of 200 spins and determine the dependence of K on the
magnetization M. The K-M relation changes drastically depending on the ratio of
the coupling constants in the leg and rung directions. We also discuss
implications of these results to experiments on the nuclear spin relaxation
rate 1/T_1 and dynamical spin structure factors.
