Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons
arXiv:2101.11065 · doi:10.1016/j.aop.2021.168526
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 [Phys. Rev. Lett. {\bf 125}, 027002 (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.
29 pages, 14 figures, final version as published in Localisation 2020 volume of Annals of Physics
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Cited by in corpus (8)
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- Localization of the Higgs mode at the superfluid-Mott glass transition
- Scalar susceptibility of a diluted classical XY model
- Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores
- Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems
- Finite temperature mean-field theory with intrinsic non-hermitian structures for Bose gases in optical lattices
- Amplitude mode at the superfluid-insulator transition on a random lattice