Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition

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