Fermion loops and improved power-counting in two-dimensional critical metals with singular forward scattering

Understand

We analyze general properties of the perturbation expansion for two-dimensional quantum critical metals with singular forward scattering, such as metals at an Ising nematic quantum critical point and metals coupled to a U(1) gauge field.

• We derive asymptotic properties of fermion loops appearing as subdiagrams of the contributing Feynman diagrams -- for large and small momenta.
• Substantial cancellations are found in important scaling limits, which reduce the degree of divergence of Feynman diagrams with boson legs.
• Implementing these cancellations we obtain improved power-counting estimates that yield the true degree of divergence.