Exact Results for a Spin-${\bf 1}$ lattice

Details Exact Results for a Spin-${\bf 1}$ lattice Exact Results for a Spin-${\bf 1}$ lattice

2003-06-05

arxiv.org/abs/cond-mat/0306124v1

J. Phys. Cond. Matt., 15, 4583 (2003)

Physics

Condensed Matter

Superconductivity

to appear in J. Phys. Cond. Matt

Scientific paper

10.1088/0953-8984/15/26/308

We consider a lattice of spin-1 particles with a general pairwise interaction $ [ {\rm cos} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1}) \ + {\rm sin} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1})^2 \ ]$. We show that, for a large class of lattices with even number of sites, the ground state for the region $ - {3 \pi \over 4} < \gamma < - {\pi \over 2}$ belongs to total spin $S_{\rm tot} = 0$, whereas the state of minimum excited energy but with finite $S_{\rm tot}$ belongs to $S_{\rm tot} = 2$. These results are constrasted with the generalized Marshall theorems, applicable to a bipartite lattice and $ - {\pi \over 2} < \gamma \le 0$.

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