Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to $(J_2/J_1{)}^{14}$] permit one to fix the parameters of ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$ precisely: $J_1=6.16\mathrm{}\left(10\right)\mathrm{meV}$, $x≔J_2/J_1=0.603\mathrm{}\left(3\right)$, $J_{\perp }=1.3\mathrm{}\left(2\right)\mathrm{meV}$. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at $x=0.63\mathrm{}$ indicates a transition towards another phase. The possible nature of this phase is discussed.

• Received 19 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.3958