Two-point function of a $d=2$ quantum critical metal in the limit   $k_F\rightarrow\infty$, $N_f\rightarrow 0$ with $N_fk_F$ fixed
  We show that the fermionic and bosonic spectrum of $d=2$ fermions at finite density coupled to a critical boson can be determined non-perturbatively in the combined limit $k_F\rightarrow {\infty}$, $N_f \rightarrow 0$ with $N_fk_F$ fixed. In this double scaling limit, the boson two-point function is corrected, but only at one-loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched $N_f\rightarrow 0$ result. For $\omega \rightarrow 0$ with $k$ fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory. 
Petter S\"aterskog, Balazs Meszena, Koenraad Schalm
cond-mat.str-el hep-th