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We analyze quantum fluctuation effects at the onset of charge or spin densitywave order in two-dimensional metals with an incommensurate $2k_F$ wave vectorconnecting a single pair of hot spots on the Fermi surface. We compute themomentum and frequency dependence of the fermion self-energy near the hot spotsto leading order in a fluctuation expansion (one loop). Non-Fermi liquidbehavior with anomalous frequency scaling and a vanishing quasi particle weightis obtained. The momentum dependence yields a divergent renormalization of theFermi velocity and a flattening of the Fermi surface near the hot spots. Goingbeyond the leading order calculation we find that the one-loop result is notself-consistent. We show that any momentum-independent self-energy with anon-Fermi liquid frequency exponent wipes out the peak of the polarizationfunction at the $2k_F$ wave vector, and thus destroys the mechanism favoring$2k_F$ density waves over those with generic wave vectors. However, a $2k_F$density wave quantum critical point might survive in presence of a sufficientlyflat renormalized Fermi surface.

Fluctuation effects at the onset of $\bf 2k_F$ density wave order with one pair of hot spots in two-dimensional metals