Phase diagram of the extended chequerboard $J-Q$ model

Abstract

The chequerboard $J-Q$ model was proposed to describe the direct phase transition from the antiferromagnetic (AFM) state to the plaquette-sin glet (PS) solid state observed in SrCu$_2({\rm BO}_3)_2$. In this paper, we present a Monte Carlo study of the ground state of an extended ve rsion of this model. For all parameters investigated, we find only a direct first-order phase transitions from the AFM to the PS phase, with no intermediate phase between them. On the transition line, the system exhibits an emergent $O(4)$ symmetry. Furthermore, we find that the Bi nder ratio of the columnar valence-bond solid state can be used to locate the phase transition. It exhibits a monotonic finite-size scaling b ehavior, allowing for a precise determination of the transition point.