Generalized Hertz action and quantum criticality of two-dimensional Fermi systems

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector Q= 0. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian momentum-shell renormalization group (RG) theory capturing the infrared scaling should be formulated keeping Q as a flowing, scale-dependent quantity. At the quantum critical point, scaling controlled by the dynamical exponent z=3 is overshadowed by a broad scaling regime characterized by a lower value of z 2. This in particular offers an explanation of the results of quantum Monte Carlo simulations pertinent to the electronic nematic quantum critical point.