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 ∑(k, ω) ≈ (k) to ∑(k, ω) ≈ (ω), where k and ω 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.