Ground-state properties of axially anisotropic quantum Heisenberg chains

The ground state and low-lying excited states of a one-dimensional Heisenberg model with axial anisotropy are studied by extrapolation from finite lattices. The ground-state properties and the phase diagram are determined for quantum spins, especially for $S=\frac{1}{2}, 1, \mathrm{and} \frac{3}{2}$. Higher spin values do not give new features in the phase diagram. the limitations of finite-lattice extrapolation are discussed in connection with the possibility of a singlet phase for the $S=1\mathrm{}$ isotropic Heisenberg antiferromagnet.