Higgs amplitude mode in the vicinity of a (2+1)-dimensional quantum critical point

We study the Higgs amplitude mode in the relativistic quantum O(N) model in two space dimensions. Using the nonperturbative renormalization group we compute the O(N)-invariant scalar susceptibility in the vicinity of the zero-temperature quantum critical point. In the zero-temperature ordered phase, we find a well-defined Higgs resonance for N = 2 with universal properties in agreement with quantum Monte Carlo simulations. The resonance persists at finite temperature below the Berezinskii-Kosterlitz-Thouless transition temperature. In the zero-temperature disordered phase, we find a maximum in the spectral function which is, however, not related to a putative Higgs resonance. Furthermore we show that the resonance is strongly suppressed for N >= 3.