Stability of Dirac Liquids with Strong Coulomb Interaction

We develop and apply the Diagrammatic Monte Carlo technique to address the problem of stability of the Dirac liquid state (in a graphene type system) against strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or RPA treatments, with diametrically opposite conclusions. Our calculations aim at the approximations-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size $L$ (up to $ln(L) \sim 40$), the coupling constant always flows towards zero; i.e. the two dimensional Dirac liquid is an asymptotically free $T=0$ state with divergent Fermi velocity.