Spin Gap in Two-Dimensional Heisenberg Model for CaV$_4$O$_9$

Abstract

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.Comment: 8 pages, 6 figures available upon request (Revtex