Stability of Dirac Liquids with Strong Coulomb Interaction

Abstract

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.

5 pages, 4 figures

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• Fermi-liquid ground state of interacting Dirac fermions in two dimensions
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• Interaction-enhanced nesting in Spin-Fermion and Fermi-Hubbard models
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Bridging the gap between numerics and experiment in free standing graphene
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