Fermi liquids beyond the forward-scattering limit: The role of nonforward scattering for scale invariance and instabilities

Landau Fermi liquid theory is a fixed-point theory of metals that includes the forward-scattering amplitudes as exact marginal couplings. However, the fixed-point theory that only includes the strict forward scatterings is nonlocal in real space. In this paper, we revisit the Fermi liquid theory for charge-neutral fermions using the field-theoretic functional renormalization group formalism and show how the scale-invariant fixed point emerges …