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Excitation spectra of disordered dimer magnets near quantum criticality

For coupled-dimer magnets with quenched disorder, we introduce a generalization of the bond-operator method, appropriate to describe both singlet and magnetically ordered phases. This allows for a numerical calculation of the magnetic excitations at all energies across the phase diagram, including the strongly inhomogeneous Griffiths regime near quantum criticality. We apply the method to the bilayer Heisenberg model with bond randomness and characterize both the broadening of excitations and the transfer of spectral weight induced by disorder. Inside the antiferromagnetic phase this model features the remarkable combination of sharp magnetic Bragg peaks and broad magnons, the latter arising from the tendency to localization of low-energy excitations.