Anomalous thermal broadening in the Shastry-Sutherland model and SrCu$_2($BO$_3)_2$

TL;DR

This paper demonstrates that the anomalous thermal broadening of triplon modes in SrCu$_2$(BO$_3)_2$ can be explained by the Shastry-Sutherland model using advanced numerical simulations, revealing a small energy scale responsible for the effect.

Contribution

The authors develop a matrix-product state based numerical method to accurately simulate dynamical spectral functions at finite temperatures for the Shastry-Sutherland model.

Findings

The broadening of triplon modes is captured by the model.

A small energy scale between single and bound triplon states causes the broadening.

Numerical simulations match experimental observations.

Abstract

The quantum magnet SrCu$_2($BO$_3)_2$ and its remarkably accurate theoretical description, the spin-$1/2$ Shastry-Sutherland model, host a variety of intriguing phenomena such as a dimer ground state with a nearly flat band of triplon excitations, a series of magnetization plateaux, and a possible pressure-induced deconfined quantum critical point. One open puzzle originating from inelastic neutron scattering and Raman experiments is the anomalous broadening of the triplon modes at relatively low temperatures compared to the triplon gap $\Delta$. We demonstrate that the experimentally observed broadening is captured by the Shastry-Sutherland model. To this end, we develop a numerical simulation method based on matrix-product states to simulate dynamical spectral functions at nonzero temperatures accurately. Perturbative calculations identify the origin of this phenomenon as a small energy scale compared to $\Delta$ between single triplon and bound triplon states at the experimentally relevant model parameters.