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

TL;DR

This study uses large-scale numerical diagonalization to precisely determine the phase boundary of the Shastry-Sutherland model, providing an accurate ratio for the dimer phase edge and comparing it with experimental ESR data.

Contribution

The paper presents the first large-scale diagonalization study on the Shastry-Sutherland model to accurately locate the dimer phase boundary.

Findings

Edge ratio r=0.6754(2) determined

Finite-size clusters of 44 and 48 spins used

Comparison with ESR experimental results

Abstract

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.