Non-Fermi liquid fixed points and anomalous Landau damping in a quantum critical metal

We present a functional renormalization group calculation of the properties of a quantum critical metal in $d=2$ spatial dimensions. Our theory describes a general class of Pomeranchuk instabilities with $N_b$ flavors of boson. At small $N_b$ we find a family of fixed points characterized by weakly non-Fermi-liquid behavior of the conduction electrons and $z \approx 2$ critical dynamics for the order parameter fluctuations, in agreement with the scaling observed by Schattner et al. [Phys. Rev. X 6, 031028 (2016)] for the Ising-nematic transition. Contrary to recent suggestions that this represents an intermediate regime en route to the scaling limit, our calculation suggests that this behavior may persist all the way to the critical point. As the number of bosons $N_b$ is increased, the model's fixed-point properties cross over to $z \approx 1$ scaling and non-Fermi-liquid behavior similar to that obtained by Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].