Stability of Dirac Liquids with Strong Coulomb Interaction

TL;DR

This paper uses Diagrammatic Monte Carlo to rigorously analyze the stability of Dirac liquids in graphene-like systems against strong Coulomb interactions, demonstrating their asymptotic freedom at zero temperature.

Contribution

It provides an approximation-free, controlled study of Coulomb interactions in Dirac liquids, resolving conflicting previous theoretical results.

Findings

Coupling constant flows to zero with increasing system size

Dirac liquid is asymptotically free at zero temperature

Fermi velocity diverges as system size grows

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.