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arXiv:2101.11065 · Annals of Physics

Inhomogeneous mean-field approach to collective excitations near the superfluid–Mott glass transition

Martin Puschmann, João C. Getelina, José A. Hoyos, Thomas Vojta

Published May 31, 2021• 9 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2021.168526

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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.
The Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.