Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids

Abstract

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: ${\mathcal{C}}^{\ast }=(92-9{\pi }^2)/(18\pi )$ and the anomalous dimension of the fermion field: ${\gamma }_{\psi }(\bar{\alpha },\xi )=2\bar{\alpha }(1-3\xi )/3-16\left({\zeta }_2{N}_F+4/27\right){\bar{\alpha }}^2+O({\bar{\alpha }}^3)$, where $\bar{\alpha }=e^2/(4\pi {)}^2$ and $\xi$ is the gauge-fixing parameter.

(v2) Published in PRD. Some references added. No change in results. (v1) LaTeX file with feynMF package. 15 pages, 4 figures

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Cited by in corpus (17)

• Multi-loop techniques for massless Feynman diagram calculations
• On the exact quantum scale invariance of three-dimensional reduced QED theories
• On Marginal Operators in Boundary Conformal Field Theory
• Comments on the Chern-Simons photon term in the QED description of graphene
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED
• Anisotropic fixed points in Dirac and Weyl semimetals
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Chiral symmetry restoration in RQED at finite temperature in the supercritical coupling regime
• Effects of the two-dimensional Coulomb interaction in both Fermi velocity and energy gap for Dirac-like electrons at finite temperature
• Non-perturbative field theoretical aspects of graphene and related systems
• Reduced QED with few planes and fermion gap generation
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities
• Supersymmetric Graphene on Squashed Hemisphere
• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation