Abstract
Spontaneous trimerization of the one-dimensional spin-l Heisenberg-biquadratic model is discussed in terms of a valence-bond (VB) analysis. A spin-wave theory based on a simple trimer VB state is developed and applied to the model. Within the theory a self-consistent picture is obtained: the system is trimerized for an extended region of couplings, with a non-zero energy gap that collapses at both ends of the region. Agreement with the exact results of Lai and Sutherland is found at one end of the region.
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