Third Boundary of the Shastry–Sutherland Model by Numerical Diagonalization

The Shastry–Sutherland model — the S = 1/2 Heisenberg antiferromagnet on the square lattice accompanied by orthogonal dimerized interactions — is studied by the numerical-diagonalization method. Large-scale calculations provide results for larger clusters that have not been reported yet. The present study successfully captures the phase boundary between the dimer and plaquette-singlet phases and clarifies that the spin gap increases once when the interaction forming the square lattice is increased from the boundary. Our calculations strongly suggest that in addition to the edge of the dimer phase given by J2/J1 ∼ 0.675 and the edge of the Neel-ordered phase given by J2/J1 ∼ 0.76, there exists a third boundary ratio J2/J1 ∼ 0.70 that divides the intermediate region into two parts, where J1 and J2 denote dimer and square-lattice interactions, respectively.