  Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered
within the many-body perturbation theory developed from the exactly solved
spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising
interdimer interactions. The former model is widely used for a description of
magnetic properties of the layered compound SrCu$_2$(BO$_3$)$_2$, which
exhibits a series of fractional magnetization plateaux at sufficiently low
temperatures. Using the novel type of many-body perturbation theory we have
found the effective model of interacting triplet excitations with the extended
hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization
plateaux for moderate values of the interdimer coupling. A possible existence
of a striking quantum phase of bound triplons is also revealed at low enough
magnetic fields.
