Laboratoire de Physique Théorique
Toulouse - UMR 5152

We present the application of the non-perturbative functional renormalization group (FRG) to the relativistic quantum O(N) model in two space dimensions. This model describes the critical regime of many condensed-matter systems including quantum antiferromagnets and the superfluid—Mott-insulator transition of bosons in an optical lattice. We consider the universal equation of state (which, thanks to the quantum-classical mapping, can be compared with Monte Carlo simulations of classical 3D systems in a finite geometry), the amplitude "Higgs" mode and the zero-temperature conductivity. In particular we discuss recent progress towards the computation of real-frequency correlation functions avoiding the analytical continuation of imaginary-frequency numerical data.