Localization of the Higgs mode at the superfluid-Mott glass transition

Abstract

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 XY 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 conventional power-law type. The computed spectral densities exhibit a broad, non-critical 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.

11 pages, 8 figures

References in corpus (12)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Amplitude / Higgs Modes in Condensed Matter Physics
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• The critical exponents of the superfluid transition in He4
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Theory of smeared quantum phase transitions
• Particle-hole symmetry and the dirty boson problem
• Percolation quantum phase transitions in diluted magnets
• Quantum phase transitions of the diluted O(3) rotor model
• Quantum critical behavior of the superfluid-Mott glass transition
• Emerging criticality in the disordered three-color Ashkin-Teller model
• Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons

Cited by in corpus (4)

• Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons
• Scalar susceptibility of a diluted classical XY model
• Amplitude mode at the superfluid-insulator transition on a random lattice
• Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems