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Fermion dispersion renormalization in a two-dimensional semi-Dirac semimetal

We present a non-perturbative study of the quantum many-body effects caused by the long-range Coulomb interaction in a two-dimensional semi-Dirac semimetal. This kind of semimetal may be realized in deformed graphene and a class of other realistic materials. In the non-interacting limit, the dispersion of semi-Dirac fermion is linear in one direction and quadratic in the other direction. When the impact of Coulomb interaction is taken into account, such a dispersion can be significantly modified. To reveal the correlation effects, we first obtain the exact self-consistent Dyson-Schwinger equation of the full fermion propagator and then extract the momentum dependence of the renormalized fermion dispersion from the numerical solutions. Our results show that the fermion dispersion becomes linear in two directions. These results are compared to previous theoretical works on semi-Dirac semimetals.