We study the collective excitations, i.e., the Goldstone (phase) mode and the Higgs (amplitude) mode, near the superfluid-Mott glass quantum phase transition in a two-dimensional system of disordered bosons. Using Monte Carlo simulations as well as an inhomogeneous quantum mean-field theory with Gaussian fluctuations, we show that the Higgs mode is strongly localized for all energies, leading to a noncritical scalar response. In contrast, the lowest-energy Goldstone mode undergoes a striking delocalization transition as the system enters the superfluid phase. We discuss the generality of these findings and experimental consequences, and we point out potential relations to many-body localization.
M. Puschmann et al., "Collective Modes at a Disordered Quantum Phase Transition," Physical Review Letters, vol. 125, no. 2, American Physical Society, Jul 2020.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.125.027002
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10 Jul 2020