We study the “Higgs” amplitude mode in the relativistic quantum $O\left(N\right)$ model in two space dimensions. Using the nonperturbative renormalization group we compute the $O\left(N\right)$-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 $N\ge 3$.

• Received 14 February 2014
• Revised 16 April 2014

DOI:https://doi.org/10.1103/PhysRevB.89.180501