The effect of vertex corrections on the possibility of chiral symmetry breaking, induced by long-range Coulomb repulsion in graphene

Understand

In this paper we consider the possibility of chiral (charge or spin density wave) symmetry breaking in graphene due to long-range Coulomb interaction by comparing the results of the Bethe-Salpeter and functional renormalization-group approaches.

• The former approach performs summation of ladder diagrams in the particle-hole channel, and reproduces the results of the Schwinger-Dyson approach for the critical interaction strength of the quantum phase transition.
• The renormalization-group approach combines the effect of different channels and allows to study the role of vertex corrections.
• The critical interaction strength, which is necessary to induce the symmetry breaking in the latter approach is found in the static approximation to be $\alpha _{c}=e^{2}/(\epsilon v_{F})\approx 1.05$ without considering the Fermi velocity renormalization, and $\alpha _{c}=3.7$ with accounting the renormailzation of the Fermi velocity.