Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

Abstract

We consider the 2D Hubbard model on the honeycomb lattice, as a model for single layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its non-interacting value and turns out to be isotropic. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast with the predictions based on relativistic or continuum approximations.

4 pages, 1 figure; version published on Phys. Rev. B; erratum added

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Cited by in corpus (22)

• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Absence of interaction corrections in graphene conductivity
• Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Universality of conductivity in interacting graphene
• Lattice gauge theory model for graphene
• Lattice quantum electrodynamics for graphene
• Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Topological phase transitions and universality in the Haldane-Hubbard model
• Strongly Interacting Weyl Semimetals: Stability of the Semimetallic Phase and Emergence of Almost Free Fermions
• Ground state properties of graphene in Hartree-Fock theory
• Anomalous behavior in an effective model of graphene with Coulomb interactions
• Interacting Weyl semimetals on a lattice
• Symmetry Enforced Stability of Interacting Weyl and Dirac Semimetals
• Weyl semimetallic phase in an interacting lattice system
• Renormalization theory of a two dimensional Bose gas: quantum critical point and quasi-condensed state
• Correlated Dirac semimetal by periodized cluster dynamical mean-field theory
• Low dimensional interacting bosons
• Bridging the gap between numerics and experiment in free standing graphene
• Non-Fermi Liquid Behaviors in the Hubbard model on the Honeycomb lattice