Interactions and Renormalization of Semi-Dirac Fermions

We develop full renormalization group (RG) analysis of 2D semi-Dirac
fermions at quantum criticality. Such systems have quadratic dispersion in
one direction and linear, Dirac-like in the other, and appear in numerous
physical situations. However, Coulomb interactions lead to very strong spectrum
renormalization due to the appearance of log squared contributions.
At low energies, our RG analysis at one loop level shows that interactions tend to restore
the Dirac dispersion in both directions. This somewhat surprising conclusion differs
from results based on 1/N loop expansions, which therefore might be, in our view,
of questionable value to physical systems. We also discuss interaction tendencies away
from criticality. Overall we expect wide-ranging implications from our analysis for
a variety of materials which sit right at, or close by, semi-Dirac criticality.