Exact Ground and Excited States of Frustrated Antiferromagnets on the Cav 4 O 9 Lattice

The experimental observation of a spin-gap in the antiferromagnetic spin2 compound CaV4O9 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 spin2 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 and hence the spin-gap can be calculated exactly and the result obtained compared with experimental data. In a different parameter regime, the dimer state is shown to be the exact ground state. PACS Nos: 75.10.Jm, 75.10.-b, 75.40.Gb Recent discovery of a spin-gap in CaV4O9[1] has given rise to a number of studies[2, 3, 4, 5, 6, 7, 8] to understand the origin of the gap. The magnetic system can be described by the antiferromagnetic (AFM) Heisenberg Hamiltonian for spins of V 4+ ions (S = 1 2 ) on a 1/5-depleted square lattice. The depleted lattice is obtained from the original square lattice by removing 1 5 of the lattice sites in a regular manner. The depleted lattice is a bipartite lattice which consists of 4-spin plaquettes connected by dimer bonds designated as A and B respectively in Fig. 1. The minimal model to describe the system is the Heisenberg Hamiltonian