  We aim to understand how the spectrum of semi-Dirac fermions is renormalized
due to long-range Coulomb electron-electron interactions at a topological
Lifshitz transition, where two Dirac cones merge. At the transition, the
electronic spectrum is characterized by massive quadratic dispersion in one
direction, while it remains linear in the other. We have found that, to lowest
order, the unconventional log squared (double logarithmic) correction to the
quasiparticle mass in bare perturbation theory leads to resummation into strong
mass renormalization in the exact full solution of the perturbative
renormalization group equations. This behavior effectively wipes out the
curvature of the dispersion and leads to Dirac cone restoration at low energy:
the system flows towards Dirac dispersion which is anisotropic but linear in
momentum, with interaction-depended logarithmic modulation. The Berry phase
associated with the restored critical Dirac spectrum is zero - a property
guaranteed by time-reversal symmetry and unchanged by renormalization. Our
results are in contrast with the behavior that has been found within the
large-$N$ approach.
