Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution

Abstract

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution.

24 pages, 7 figures

References in corpus (24)

• The electronic properties of graphene
• Exact evolution equation for the effective potential
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• High-performance functional renormalization group calculations for interacting fermions
• Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Phase diagram of the Kane-Mele-Coulomb model
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Interaction driven metal-insulator transition in strained graphene
• Interacting electrons on trilayer honeycomb lattices
• Correlated spinless fermions on the honeycomb lattice revisited
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice
• Parametrization of Nambu vertex in a singlet superconductor
• Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization
• Electronic Instabilities of the AA-Honeycomb Bilayer
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

Cited by in corpus (35)

• High-performance functional renormalization group calculations for interacting fermions
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Quantum Order-by-Disorder in Strongly Correlated Metals
• Reference results for the momentum space functional renormalization group
• Functional renormalization group for a large moiré unit cell
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions
• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems
• Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Competing Orders and Unconventional Criticality in the Su-Schrieffer-Heeger Model
• Truncated unity functional renormalization group for multiband systems with spin-orbit coupling
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study
• Effect of exchange interaction on electronic instabilities in the honeycomb lattice: A functional renormalization group study
• Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
• Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Generalized dynamical mean-field theory of two-subalttice systems with non-local interactions and its application to study charge and spin correlations in graphene
• Hidden Charge Order of Interacting Dirac Fermions on the Honeycomb Lattice
• Consistent combination of truncated-unity functional renormalization group and mean-field theory
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
• Influence of hopping selfenergy and quasiparticle degradation on the antiferromagnetic ordering in the bilayer honeycomb Hubbard model
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• Stability of the Néel quantum critical point in the presence of Dirac fermions
• Hubbard Model on the Honeycomb Lattice with an Indefinite Long-Range Interaction
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Spin bond order driven by extended repulsive interactions in doped graphene