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Correlated decay of triplet excitations in the Shastry-Sutherland compound SrCu$_2$(BO$_3$)$_2$

The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu$_2$(BO$_3$)$_2$ is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature while the integrated spectral weight can be explained by an isolated dimer model up to 10~K. Analyzing this anomalous spectral line-shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the underlying mechanism through a simple yet quantitatively accurate model of correlated decay of triplons: an excited triplon is long-lived if no thermally populated triplons are near-by but decays quickly if there are. The phenomenon is a direct consequence of frustration induced triplon localization in the Shastry--Sutherland lattice.