Non-perturbative renormalization group calculation of the quasi-particle velocity and the dielectric function of graphene

Using a non-perturbative functional renormalization group approach we calculate the renormalized quasi-particle velocity $v(k)$ and the static dielectric function $ϵ(k)$ of suspended graphene as functions of an external momentum $k$. Our numerical result for $v(k)$ can be fitted by $v ( k ) / v_F = A + B \ln ( \Lambda_0 / k )$,where$v_F$ is the bare Fermi velocity, ${\mathrm{\Lambda }}_0$ is an ultraviolet cutoff, and $A=1.37$, $B=0.51$ for the physically relevant value ($e^2\mathrm{/}{v}_F=2.2$) of the coupling constant. In contrast to calculations based on the static random-phase approximation, we find that $ϵ(k)$ approaches unity for $k\to 0$. Our result for $v(k)$ agrees very well with a recent measurement by Elias et al. [Nat. Phys. 7, 701 (2011)].