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Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model -- including additional interactions and exchange anisotropy -- over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field -- qualitatively similar to experimentally observed low-temperature phases in ErB$_4$. Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results will provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB$_4$.