Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene

Abstract

We investigate magnetic and charge correlations in graphene by using the formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. First, we map the average non-local interaction onto the effective static interaction between different sublattices, which is treated together with the local interaction within an effective "two-orbital" local model. The remaining part of the non-local interaction is considered by introducing an effective retarded interaction within the E-DMFT approach. The non-local susceptibilities in charge and spin channel are further evaluated in the ladder approximation. We verify the applicability of the proposed method to describe the effect of uniformly screened long-range Coulomb potential $\propto 1/r$, as well as screened realistic long-range electron interaction [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the developed approach describes a competition of semimetal, spin density wave (SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram is in a good agreement with recent results of functional renormalization group (fRG) for finite large graphene nanoflakes and scaling analysis of quantum Monte Carlo data on finite clusters. Similarly to the previously obtained results within the fRG approach, the realistic screening of Coulomb interaction by $\sigma$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential.

arXiv comment9 pages, 5 figures

References in corpus (56)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Dielectric function, screening, and plasmons in 2D graphene
• Graphene bilayer with a twist: electronic structure
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Strength of effective Coulomb interactions in graphene and graphite
• Interactions and phase transitions on graphene's honeycomb lattice
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Is graphene in vacuum an insulator?
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• Energy resolution and discretization artefacts in the numerical renormalization group
• Extended Dynamical Mean Field Theory and GW method
• Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model
• Lattice field theory simulations of graphene
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Spatial Correlations in Dynamical Mean Field Theory
• Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model
• Electronic spectrum of twisted bilayer graphene
• Excitonic instability in two-dimensional degenerate semimetals
• Gap generation and semimetal-insulator phase transition in graphene
• Effective action approach to strongly correlated fermion systems
• The role of electron-electron interactions in two-dimensional Dirac fermions
• Supercritical Coulomb center and excitonic instability in graphene
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Massive Dirac fermions in single-layer graphene
• Ab initio dynamical vertex approximation
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Charge ordering and correlation effects in the extended Hubbard model
• Excitonic pairing between nodal fermions
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical Behavior in Graphene with Coulomb Interactions
• Phase diagram and Fermi-liquid properties of the extended Hubbard model on the honeycomb lattice
• Charge order and antiferromagnetism in the extended Hubbard model
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• $i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Phase diagram of the Quantum Electrodynamics of 2D and 3D Dirac semimetals
• Charge ordering and non-local correlations in the doped extended Hubbard model
• Non-local correlations in metals close to a charge order insulator transition
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Multiband Dual Fermion Approach to Quantum Criticality in the Hubbard Honeycomb Lattice
• Improved treatment of fermion-boson vertices and Bethe-Salpeter equations in non-local extensions of dynamical mean field theory
• The effect of vertex corrections on the possibility of chiral symmetry breaking, induced by long-range Coulomb repulsion in graphene
• Magnetic, charge, and transport properties of graphene nanoflakes
• Theory for the electronic structure of incommensurate twisted bilayer graphene

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