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Non-perturbative corrections to the quasiparticle velocity in graphene

Relativistic fermionic systems have physical quantities calculated by well stablished quantum electrodynamic prescriptions. In the last few years there has been an enormous interest in condensed matter systems in which the fermions exhibit relativistic dispersion, as Dirac fermions in graphene. We employ a non-perturbative method in order to obtain a non-perturbative correction to the quasiparticle velocity in graphene, and compare with the experimental data. We find a better agreement between the quasiparticle velocity corrected with non-perturbative corrections and measurements, when compared with the standard one-loop result. We also investigate the behavior of the beta function of the renormalization group theory, and find that the non-perturbative corrections do not alter the stability of the infrared fixed point found by the standard result.