Collective excitations and stability of a non-Fermi liquid state near a quantum-critical point of a metal

The spectral properties of collective excitations with finite angular momentum l for a system of interacting fermions near a Pomeranchuk quantum critical point are examined, both in the Fermi liquid and non-Fermi liquid regimes. Previous studies found that deep in the Fermi liquid regime, the spectral functions for even and odd l behave differently—the latter is suppressed compared to the former because of kinematic constraints on scattering processes. We trace the evolution of even- and odd-l spectral functions as the system crosses into the non-Fermi liquid regime.To this end, the full scaling function for the electron polarization bubble at arbitrary l is derived, which interpolates between the Fermi liquid and non-Fermi liquid regimes. We show that collective excitations for all l remain stable and causal throughout the crossover and right at the quantum critical point.