The amplitude (Higgs) mode near the two-dimensional superfluid-Mott glass quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of disordered interacting bosons onto an equivalent classical model in (2+1) dimensions and compute the scalar susceptibility of the order parameter amplitude via Monte Carlo simulation. Analytic continuation of the scalar susceptibilities from imaginary to real frequency to obtain the spectral densities is performed by a modified maximum entropy technique. Our results show that the introduction of disorder into the system leads to unconventional dynamical behavior of the Higgs mode that violates naive scaling, despite the underlying thermodynamics of the transition being of the conventional power-law type. The computed spectral densities exhibit a broad, noncritical response for all energies, and a momentum-independent dispersion for long wavelengths, indicating strong evidence for the localization of the Higgs mode for all dilutions.




This work was supported in part by the NSF under Grant No. DMR-1828489.

International Standard Serial Number (ISSN)

2469-9950; 2469-9969

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2021 American Physical Society (APS), All rights reserved.

Publication Date

01 Jul 2021

Included in

Physics Commons