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

TL;DR

This paper derives exact ground states for a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice, revealing specific magnetization plateaus and ordering patterns, and compares these results with classical and quantum models.

Contribution

It introduces two rigorous methods to find exact ground states of the model, providing new insights into its magnetization behavior and ordering phenomena.

Findings

Magnetization curve with two intermediate plateaus at 1/3 and 1/2 saturation

Stripe and checkerboard orderings of singlets and triplets

Comparison with classical and quantum models

Abstract

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggested Ising-Heisenberg model.