Quantum phase transition in the Plaquette lattice with anisotropic spin exchange

I study the influence of anisotropic spin exchange on a quantum phase transition in the Plaquette lattice driven by the purely quantum effect of singlet formation. I study the influence of i) a Dzyaloshinskii-Moriya exchange and ii) four spin exchange on the transition point by evaluating spin--spin correlations and the spin gap with exact diagonalization. The results point to a stabilization of the Neel-like long range order when the Dzyaloshinskii-Moriya exchange is added, whereas the four-spin exchange might stabilize the singlet order as well as the Neel-like order depending on its strength.