Spin gap in CaV4O9: A large-Sapproach

We study the stability of the four-site plaquette order in a model recently introduced by Katoh and Imada to explain the spin gap observed in ${\mathrm{Ca}{\mathrm{V}}_4)}_9$. We show that all relevant types of order (four-site plaquette, dimerized, Néel) can be described within the framework of Schwinger-boson mean-field theory, and we make predictions regarding their relative stability. The results are compared to exact diagonalization of finite clusters.