Ground-State Phase Diagram for the Three-Dimensional Orthogonal-Dimer System

We investigate quantum phase transitions in the three-dimensional orthogonal-dimer system of the compound $\mathrm{S}\mathrm{r}\mathrm{C}{\mathrm{u}}_2(\mathrm{B}{\mathrm{O}}_3{)}_2$ by means of the series expansion technique. We then discuss the phase diagram where the dimer phase, the Haldane phase, the frustration-induced disordered phase and the magnetically ordered phase compete with each other. It is found that the compound $\mathrm{S}\mathrm{r}\mathrm{C}{\mathrm{u}}_2(\mathrm{B}{\mathrm{O}}_3{)}_2$ is located in the dimer phase close to the phase boundary.