Quantum critical behavior near a density-wave instability in an   isotropic Fermi liquid
  We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector q_c. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) ~ Sigma(k) to Sigma(k,omega) ~ Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before, i.e., the Fermi liquid survives up to the critical point. 
Andrey V. Chubukov, Victor Galitski, Victor M. Yakovenko