1993 年 62 巻 9 号 p. 3257-3265
The one-dimensional S=1 anisotropic antiferromagnetic Heisenberg model with next-nearest as well as nearest-neighbor exchange intearction is studied with particular emphasis on the effect of the frustration. The ground-state phase diagram and the low-lying excitations are examined by use of the bosonization method and the self-consistent harmonic approximation. It turns out that the frustration works in stabilizing the Haldane phase against the Neel phase, since its effect on the latter phase is larger. The large-D phase is almost unaffected by the frustration, resulting in its relative stability against other phases. The excitation gap in the Haldane phase (Haldane gap) is found to be reduced by the frustration near the boundary to the large-D phase, while it increases in the vicinity of the Neel phase.
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