Coulomb interactions in systems of generalized semi-Dirac fermions

Interactions have strong effects in systems with flat bands. We examine the role of Coulomb interactions in two-dimensional chiral anisotropic quasiparticles that disperse linearly in one direction and have relatively flat bands near the neutrality point in the other direction, dispersing with an arbitrary, positive, even power law $2n\ensuremath{\ge}2$. As in the conventional semi-Dirac case $(n=1)$, we show, using the renormalization group, that strong logarithmic divergences in the self-energy of generalized semi-Dirac fermions resum and lead to a restoration of linearity in the spectrum for arbitrary $n$ over a sizable energy window in the perturbative regime. We discuss those results in light of previous nonperturbative large-${N}_{f}$ results and address the implications for physical observables.