Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and quadratic single-ion anisotropies in an external field are studied, for special choices of the two kinds of anisotropies. In particular, the phase diagram includes antiferromagnetic, spin-liquid (or spin-flop), (10), and supersolid (or biconical) phases. Especially, new features of the spin-liquid and supersolid phases are discussed. Properties of the quantum chains are compared to those of corresponding classical spin chains.
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