Quantum Phase Transitions in the Shastry-Sutherland Model for $\rm\bf SrCu_2 (BO_3)_2$

Abstract

We investigate the quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for $\rm SrCu_2(BO_3)_2$ by using the series expansion method. It is found that a novel spin-gap phase, which is adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known so far. When the ratio of the competing exchange couplings $\alpha(=J'/J)$ is varied, this spin-gap phase exhibits the first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point $\alpha_{c1}=0.677(2)$ ($\alpha_{c2}=0.86(1)$). Our results shed light on some controversial arguments about the nature of the quantum phase transitions in this model.