Large-Scale Numerical-Diagonalization Study of the Shastry-Sutherland Model

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.