Dynamic Structure Factor of the Two-Dimensional Shastry-Sutherland Model

We calculate the two-triplon contribution to the dynamic structure factor of the two-dimensional Shastry-Sutherland model, realized in ${\mathrm{S}\mathrm{r}\mathrm{C}\mathrm{u}}_2({\mathrm{B}\mathrm{O}}_3{)}_2$, by means of perturbative continuous unitary transformations. For realistic parameters we find flat bound two-triplon bands. These bands show large weight in the structure factor depending strongly on momentum. So our findings permit a quantitative understanding of high precision inelastic neutron scattering experiments.

Figure 1

Shastry-Sutherland model with spin $1/2$ on the dots; dimers are solid lines. The microscopic angles and distances apply to ${\mathrm{S}\mathrm{r}\mathrm{C}\mathrm{u}}_2({\mathrm{B}\mathrm{O}}_3{)}_2$ according to Ref. 1. The primitive vectors $\mathbf{a}$ and $\mathbf{b}$ span the dimer lattice ${\Gamma }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ (all dimers taken as equal), while $\tilde{\mathbf{a}}$ and $\tilde{\mathbf{b}}$ span the lattice ${\Gamma }_{\mathrm{A}\mathrm{B}}$ distinguishing horizontal and vertical dimers.

Figure 2

Two-triplon contribution to the spectral densities of the observable $\mathcal{N}(\mathbf{q})$ representing the INS on ${\mathrm{S}\mathrm{r}\mathrm{C}\mathrm{u}}_2({\mathrm{B}\mathrm{O}}_3{)}_2$ for two sets of parameters. For clarity, a broadening of $0.02J_1$ is used. The inaccuracy of the peak positions due to the extrapolation is about 2.5%.

Figure 3

Color-coded spectral density of $\mathcal{N}$ in the energy-momentum plane. Intensities as indicated by the scale on the right-hand side. Parameters are the same as in Fig. 2.