Localization of the Higgs mode at the superfluid-Mott glass quantum phase transition

We study the effects of disorder on the collective excitations near the superfluid-Mott glass quantum phase transition in a system of disordered bosons. Via large-scale Monte Carlo methods, we calculate relevant dynamical susceptibilities to study the Higgs (amplitude) and goldstone (phase) modes of the order parameter across the quantum critical point. We show that the introduction of disorder localizes the Higgs mode in the superfluid phase in both two and three spatial dimensions. We explore experimental ramifications of the effects of disorder on these modes and discuss the broader implications of unconventional dynamics in disordered quantum phase transitions.