Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2

The two dimensional Heisenberg model for SrCu_2(BO_3)_2 has the exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N'{e}el ordered state is determined. Analysis of the experimental data shows that SrCu_2(BO_3)_2 has the dimer ground state but is close to the transition point, which leads to the unusual temperature dependence of the susceptibility. Almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.