The $S=1/2$ Heisenberg antiferromagnet on the orthogonal-dimer lattice (Shastry-Sutherland model) is studied by the Lanczos diagonalization method. The properties of this model are determined by the ratio of two interactions, namely, $r=J_2/J_1$, where $J_1$ denotes the amplitude of spin interactions at orthogonal dimers and the interactions represented by $J_2$ form the square lattice. We focus our attention on the edge of the phase in which the dimer state is realized as the exact ground state. Our large-scale calculations of diagonalizations treating finite-size clusters including 44 and 48 spin sites successfully detect the target edge. Our conclusion is that the ratio for the edge is $r= 0.6754(2)$. This estimate is compared with an experimental result from electron spin resonance measurements.

中文翻译：

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Shastry-Sutherland模型的大规模数值对角化研究

通过Lanczos对角化方法研究正交二聚体晶格（Shastry-Sutherland模型）上的$S=1/2$海森堡反铁磁体。该模型的性质由两个相互作用的比率决定，即$r=J_2/J_1$，其中$J_1$ 表示正交二聚体处自旋相互作用的幅度，$J_2$ 表示的相互作用形成正方形晶格。我们将注意力集中在二聚体状态被实现为精确基态的阶段边缘。我们处理包括 44 和 48 个自旋点在内的有限大小簇的对角化的大规模计算成功地检测到目标边缘。我们的结论是边缘的比率是 $r= 0.6754(2)$。将该估计与电子自旋共振测量的实验结果进行比较。