Third boundary of the Shastry-Sutherland Model by Numerical Diagonalization

TL;DR

This study uses large-scale numerical diagonalization to explore the phase boundaries of the Shastry-Sutherland model, revealing a third boundary in the phase diagram and clarifying the behavior of the spin gap.

Contribution

It identifies a previously unreported third boundary in the phase diagram of the Shastry-Sutherland model using advanced numerical methods.

Findings

Confirmed the phase boundary between dimer and plaquette-singlet phases.

Discovered a third boundary ratio at J2/J1 ≈ 0.70 dividing the intermediate region.

Observed the increase of the spin gap when the square-lattice interaction is increased.

Abstract

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 $J_{2}/J_{1}\sim 0.675$ and the edge of the N$\acute{\rm e}$el-ordered phase given by $J_{2}/J_{1}\sim 0.76$, there exists a third boundary ratio $J_{2}/J_{1}\sim 0.70$ that divides the intermediate region into two parts, where $J_{1}$ and $J_{2}$ denote dimer and square-lattice interactions, respectively.