  The amplitude (Higgs) mode near the two-dimensional superfluid-Mott glass
quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of
disordered interacting bosons onto an equivalent classical XY model in (2+1)
dimensions and compute the scalar susceptibility of the order parameter
amplitude via Monte Carlo simulation. Analytic continuation of the scalar
susceptibilities from imaginary to real frequency to obtain the spectral
densities is performed by a modified maximum entropy technique. Our results
show that the introduction of disorder into the system leads to unconventional
dynamical behavior of the Higgs mode that violates naive scaling,despite the
underlying thermodynamics of the transition being of conventional power-law
type. The computed spectral densities exhibit a broad, non-critical response
for all energies, and a momentum-independent dispersion for long-wavelengths,
indicating strong evidence for the localization of the Higgs mode for all
dilutions.
