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A variational procedure with a large number of parameters is used to study the ground state of the spin-1 quantum Heisenberg chain. The different phases are identified from the symmetries and degeneracies of the ground-state wave function. Irrespective of the number of variational parameters, in this approximation the isotropic antiferromagnetic point is always on the boundary between the antiferromagnetic and planar phases. The singlet Heisenberg phase is not found.
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J. Sólyom (1985) studied this question.
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