Exact ground and excited states of frustrated antiferromagnets on the CaV_4O_9 lattice
arXiv:cond-mat/9701058 · doi:10.1103/PhysRevB.56.3149
Abstract
The experimental observation of a spin-gap in the antiferromagnetic spin-1/2 compound $CaV_4O_9$ has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.
13 pages, LaTeX, 4 figures, to appear in Phys. Rev. B