Collective modes at a disordered quantum phase transition

TL;DR

This paper investigates the behavior of collective excitations near a disordered quantum phase transition, revealing localization of the Higgs mode and delocalization of the Goldstone mode, with implications for experiments and many-body localization.

Contribution

It demonstrates the localization of the Higgs mode and the delocalization transition of the Goldstone mode in a disordered superfluid--Mott glass transition using simulations and mean-field theory.

Findings

Higgs mode is strongly localized at all energies.

Goldstone mode delocalizes at the transition.

Results suggest experimental signatures and links to many-body localization.

Abstract

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.