Spiral Phase and Phase Diagram of the $S$=1/2 XXZ Model on the Shastry-Sutherland Lattice

Abstract

We investigate the ground-state phase diagram of the $S$=1/2 XXZ model on the two-dimensional Shastry-Sutherland lattice using exact diagonalization (ED), density-matrix renormalization group (DMRG), and cluster mean-field theory (CMFT) with DMRG as a solver. In the isotropic case ($\Delta=1$), CMFT results reveal an intermediate empty plaquette (EP) phase that has a lower energy than the full plaquette (FP) phase. However, due to mean-field artifacts, CMFT alone is not suitable for accurately determining phase boundaries. Therefore, we combined three methods to map out the reliable phase diagram. Our calculations show that the EP phase narrows as $\Delta$ deviates from unity and eventually vanishes. More importantly, we identify a spiral phase at small $\Delta$, which has not been reported in previous studies. This phase is clearly captured by DMRG simulations on long cylindrical geometries. The competition between the EP, spiral, and $xy$-AFM phases near their boundaries provides a plausible explanation for the emergent spin-liquid-like behavior in RE$_2$Be$_2$GeO$_2$, while shedding new light on the role of XXZ anisotropy in the Shastry-Sutherland XXZ model.