Critical properties of spin-1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy

One dimensional S = 1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D greater than or equal to 0. The ground states of this model contain the Haldane state, large-D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and delta-dependence of the Luttinger liquid paraments K and the critical exponent nu of the energy gap.