# Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

@article{Teber2018FieldTR,
title={Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids},
author={S. Teber and Anatoly V. Kotikov},
journal={Physical Review D},
year={2018},
volume={97},
pages={074004}
}
• Published 31 January 2018
• Physics
• Physical Review D
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 graphenelike 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…

## Figures from this paper

Exact quantum scale invariance of three-dimensional reduced QED theories
• Physics
Physical Review D
• 2019
An effective quantum field theory description of graphene in the ultrarelativistic regime is given by reduced quantum electrodynamics (QED) also known as pseudo QED also known as mixed-dimensional
Field theoretic study of electron-electron interaction effects in Dirac liquids
The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac
Non-perturbative field theoretical aspects of graphene and related systems
• Physics
• 2021
In this article, we review the dynamics of charge carriers in graphene and related 2D systems from a quantum field theoretical point of view. By allowing the electromagnetic fields to propagate
Review of Electron-Electron Interaction Effects in Planar Dirac Liquids
• Physics
Theoretical and Mathematical Physics
• 2019
We review field theory studies devoted to understanding electron-electron interaction effects in condensed matter systems such as planar Dirac liquids, for example, graphene and graphene-like
Remarks on the Chern-Simons photon term in the QED description of graphene
• Physics
Physical Review D
• 2018
We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this nonlocal but still gauge-invariant theory, we can confirm that the topological
Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene
• Physics
Journal of High Energy Physics
• 2018
A bstractThe two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study
Anisotropic fixed points in Dirac and Weyl semimetals
• Physics
Physical Review B
• 2018
The effective low energy description of interacting Dirac and Weyl semimetals is that of massless quantum electrodynamics with several Lorentz breaking material parameters. We perform a
On marginal operators in boundary conformal field theory
• Physics
Journal of High Energy Physics
• 2019
Abstract The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of
Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Physics
• 2020
We study the gauge-covariance of the massless fermion propagator in reduced quantum electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another
Supersymmetric graphene on squashed hemisphere
• Physics
Journal of High Energy Physics
• 2021
Abstract We compute the partition function of $$\mathcal{N}$$ N = 2 supersymmetric mixed dimensional QED on a squashed hemisphere using localization. Mixed dimensional QED is an abelian gauge

## References

SHOWING 1-10 OF 123 REFERENCES
Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Physics
• 2015
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and
Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• Physics
• 2014
Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order
Quantum electrodynamics of particles on a plane and the Chern-Simons theory
Abstract We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in (2 + 1)- dimensional
Phase diagram of the quantum electrodynamics of two-dimensional and three-dimensional Dirac semimetals
We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms
Nonperturbative infrared dynamics of three-dimensional QED with a four-fermion interaction
• Physics
• 2001
A nonlinear Schwinger-Dyson (SD) equation for the gauge boson propagator of massless QED in one time and two spatial dimensions is studied. It is shown that the nonperturbative solution leads to a
Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Physics
• 2017
We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. Our fully nonperturbative calculation uses methods of lattice
Two-dimensional gas of massless Dirac fermions in graphene
This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene
• Physics
• 2014
We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field
Quantum Valley Hall Effect in Massive Dirac Systems Coupled to a Scalar Field
• Physics
• 2017
We use Pseudo Quantum Electrodynamics to study massive (2+1)D Dirac systems interacting electromagnetically via a U(1) gauge field in (3+1)D. It was recently found in Ref. [1], that an
Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions
• Physics
• 2017
We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the Pseudo