Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems

Abstract

We present spectral functions for the magnitude squared of the order parameter in the scaling limit of the two-dimensional superfluid to Mott insulator quantum phase transition at constant density, which has emergent particle-hole symmetry and Lorentz invariance. The universal functions for the superfluid, Mott insulator, and normal liquid phases reveal a low-frequency resonance which is relatively sharp and is followed by a damped oscillation (in the first two phases only) before saturating to the quantum critical plateau. The counterintuitive resonance feature in the insulating and normal phases calls for deeper understanding of collective modes in the strongly coupled (2+1)-dimensional relativistic field theory. Our results are derived from analytically continued correlation functions obtained from path-integral Monte Carlo simulations of the Bose-Hubbard model.

arXiv comment5 pages, 6 figures

References in corpus (21)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• The critical exponents of the superfluid transition in He4
• Visibility of the Amplitude (Higgs) Mode in Condensed Matter
• Dynamics and Thermodynamics of the Bose-Hubbard model
• Dynamical properties of ultracold bosons in an optical lattice
• Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering
• Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
• Spectral functions of the Higgs mode near two-dimensional quantum critical points
• The Higgs mode in a two-dimensional superfluid
• Universal relaxational dynamics near two-dimensional quantum-critical points
• Fate of the Higgs mode near quantum criticality
• Anomalous fluctuations in phases with a broken continuous symmetry
• Phase Diagram of Commensurate Two-Dimensional Disordered Bose Hubbard Model
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• The Amplitude Mode in the Quantum Phase Model
• Engineering Local optimality in Quantum Monte Carlo algorithms

Cited by in corpus (35)

• Raman scattering from Higgs mode oscillations in the two-dimensional antiferromagnet Ca${}_2$RuO${}_4$
• Dynamical structure factors and excitation modes of the bilayer Heisenberg model
• Dynamics and Conductivity Near Quantum Criticality
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
• Direct observation of the Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• The amplitude mode in three-dimensional dimerized antiferromagnets
• Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase
• The Nambu sum rule and the relation between the masses of composite Higgs bosons
• Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
• Higgs Mode and Magnon Interactions in 2D Quantum Antiferromagnets from Raman Scattering
• Spectral function of the Higgs mode in 4-\varepsilon dimensions
• The Massive Goldstone (Higgs) mode in two-dimensional ultracold atomic lattice systems
• Ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping
• Fano resonance through Higgs bound states in tunneling of Nambu-Goldstone modes
• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• Quantum XY criticality in a two-dimensional Bose gas near the Mott transition
• Damping of the Higgs and Nambu-Goldstone modes of superfluid Bose gases at finite temperatures
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$
• Observability of Higgs Mode in a system without Lorentz invariance
• Collective modes at a disordered quantum phase transition
• Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons
• Vector boson excitations near deconfined quantum critical points
• Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model
• Dual dynamic scaling in deconfined quantum criticality
• The halon: a quasiparticle featuring critical charge fractionalization
• Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase
• Response of the Higgs amplitude mode of superfluid Bose gases in a three dimensional optical lattice
• Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model
• Localized Higgs modes of superfluid Bose gases in optical lattices: A Guzwiller mean-field study
• Quantum critical dynamics for a prototype class of insulating antiferromagnets
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Critical Behavior and Collective Modes at the Superfluid Transition in Amorphous Systems
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Amplitude mode at the superfluid-insulator transition on a random lattice