Spectral function of the Higgs mode in 4-\varepsilon dimensions

Abstract

We investigate the amplitude (Higgs) mode of the relativistic O(N) model in the vicinity of the Wilson-Fisher quantum critical point in D=4-epsilon spacetime dimensions. We compute the universal part of the scalar spectral function near the transition, to leading non-trivial order in the ordered phase, and to next to leading order in both the disordered phase and the quantum critical regime. We find that, in the disordered phase, the spectral function has a threshold behavior with no Higgs-like peak, whereas in the ordered phase, the Higgs mode appears as a well defined resonance. The pole associated with this resonance is purely real in the D->4 limit, evolving smoothly with dimensionality to become purely imaginary at D=3 in the N->infty limit. Our results complement previous studies of the scalar spectral function, and demonstrate that the resonance found in these studies can indeed be directly identified with the Higgs mode.

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• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets
• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• Non-equilibrium quantum mechanics: A 'hot quantum soup' of paramagnons
• Damping of the Higgs and Nambu-Goldstone modes of superfluid Bose gases at finite temperatures
• Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model
• Holographic systems far from equilibrium: a review
• Unifying static and dynamic properties in 3D quantum antiferromagnets
• Response of the Higgs amplitude mode of superfluid Bose gases in a three dimensional optical lattice
• Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase
• 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
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition