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Exact ground states of a spin-1/2 Ising-Heisenberg model on theShastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimercouplings are found by two independent rigorous procedures. The first methoduses a unitary transformation to establish a mapping correspondence with aneffective classical spin model, while the second method relies on thederivation of an effective hard-core boson model by continuous unitarytransformations. Both methods lead to equivalent effective Hamiltoniansproviding a convincing proof that the spin-1/2 Ising-Heisenberg model on theShastry-Sutherland lattice exhibits a zero-temperature magnetization curve withjust two intermediate plateaus at one-third and one-half of the saturationmagnetization, which correspond to stripe and checkerboard orderings ofsinglets and polarized triplets, respectively. The nature of the remarkablestripe order relevant to the one-third plateau is thoroughly investigated withthe help of the corresponding exact eigenvector. The rigorous results for thespin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are comparedwith the analogous results for the purely classical Ising and fully quantumHeisenberg models. Finally, we discuss to what extent the critical fields ofSrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggestedIsing-Heisenberg model.

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field