Inhomogeneous Mean-Field Approach to Collective Excitations Near the Superfluid-Mott Glass Transition

Abstract

We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid–Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations (Puschmann et al. 2020). In quadratic (Gaussian) approximation, the Goldstone (phase) and Higgs (amplitude) modes completely decouple. Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation. We find that the Higgs mode is spatially localized in both phases. The corresponding scalar spectral function shows a broad peak that is noncritical in the sense that its peak frequency does not soften but remains nonzero across the quantum phase transition. In contrast, the lowest-energy Goldstone mode delocalizes in the superfluid phase, leading to a zero-frequency spectral peak. We compare these findings to the results of the quantum Monte Carlo simulations. We also relate them to general results on the localization of bosonic excitations, and we discuss the limits and generality of our approach.

Department(s)

Physics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

Published online: 31 May 2021

Keywords and Phrases

Collective excitation; Disorder; Localization; Quantum phase transition; Superfluid

International Standard Serial Number (ISSN)

0003-4916

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Elsevier, All rights reserved.

Publication Date

01 Dec 2021

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