Higgs amplitude mode in the vicinity of a (2+1)-dimensional quantum critical point: A nonperturbative renormalization-group approach

We study the Higgs amplitude mode in the relativistic quantum O(N) model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot-Mendez-Galain-Wschebor approximation (which we generalize to compute four-point correlation functions), we compute the O(N)-invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for N = 2 and 3 and determine its universal properties. No resonance is found for N >= 4. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for N = 2, the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and epsilon = 4 - (d + 1) expansion near d = 3.