The recent ESR measurement on the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 detected the pressure-induced phase transition that is expected to correspond to the quantum phase transition from the orthogonal dimer to the plaquette singlet phases.In this experiment the pressure dependence of the spin gap was observed by ESR.The ESR transition of the spin gap is forbidden due to the spin conservation law, but the Dzyaloshinsky-Moriya interaction of this compound enables the observation.Then the selection rule of the ESR transition of the spin gap in the presence ot the Dzyaloshinsky-Moriya interaction is investigated using the numerical diagonalization of the Shastry-Sutherland model.As a result, it is found that the selection rule changes at the quantum phase transition between the dimer and the plaquette singlet phases.
We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the
J1-
J2 Heisenberg model. By employing large scale Density Matrix Renormalization Group and Fully Augmented Matrix Product State calculations, combined with careful finite-size scaling, we find the phase transition between the plaquette valence bond state (PVBS) and Neel anti-ferromagnetic (AFM) phase in the pure Shastry-Sutherland model is a weak first one. This result indicates the existence of an exotic tri-critical point in the PVBS to AFM transition line in the phase diagram, as the transition in the
J1-
J2 Heisenberg model was previously determined to be continuous. We determine the location of the tri-critical point in the phase diagram at which first-order transition turns to continuous. Our generalized Shastry-Sutherland model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of Shastry-Sutherland materials like SrCu
2(BO
3)
2.