  Motivated by recent studies on the quasi-one-dimensional (1D) antiferromagnet
BaCo2V2O8, we investigate the Tomonaga-Luttinger-liquid properties of the 1D
S=1/2 XXZ Heisenberg-Ising model in magnetic fields. By using the Bethe ansatz
solution, thermodynamic quantities and the divergence exponent of the NMR
relaxation rate are calculated. We observe a magnetization minimum as a
function of temperature (T) close to the critical field. As the magnetic field
approaches the critical field, the minimum temperature asymptotically
approaches the universal relation in agreement with the recent results by Maeda
et al. in Phys. Rev. Lett. 99 (2007) 057205. We observe T-linear specific heat
below the temperature of the magnetization minimum. The field dependence of its
coefficient agrees with the results based on conformal field theory. The field
dependence of the divergence exponent of the NMR relaxation rate with
decreasing temperature is obtained, indicating a change in the critical
properties. The results are discussed in connection with experiments on
BaCo2V2O8.
