Interactions and phase transitions on graphene's honeycomb lattice

Abstract

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and of the magnetic field are discussed.

arXiv commentfour pages, one figure; few typos corrected, references added

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• Strain induced correlation gaps in carbon nanotubes
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• Quantum critical scaling of gapped phases in nodal-line semimetals
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
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• Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Superconductivity of Incoherent Electrons near the Relativistic Mott Transition in Twisted Dirac Materials
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Quantum critical scaling of altermagnetism
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• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Critical structure and emergent symmetry of Dirac fermion systems
• Edge states in bilayer graphene in a magnetic field
• Half vortex and fractional electrical charge in two dimensions
• Quantum phase transitions on the hexagonal lattice
• Fermion Mass Generation without Symmetry Breaking
• Orbital magnetization of interacting Dirac fermions in graphene
• Anisotropy engineering edge magnetism in zigzag honeycomb nanoribbons
• Emergent Supersymmetry at Large $N$
• Singular low-energy states of tilted Dirac semimetals induced by the fermion-fermion interactions
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Charge density wave in graphene: magnetic-field-induced Peierls instability
• Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point
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• Zero modes and index theorems for non-Hermitian Dirac fermions
• Competing order in the fermionic Hubbard model on the hexagonal graphene lattice
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals
• Fate of surface gaps in magnetic topological insulators
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Collective excitations of fractional quantum Hall states in monolayer graphene
• The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Projected Proca Field Theory: a One-Loop Study
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class
• Spin nematic order and superconductivity in $J_1$-$J_2$ Kondo lattice model on square lattice
• Stability of the Néel quantum critical point in the presence of Dirac fermions
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons
• Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing
• Anomalous Phase-Coherence Scaling in a Quantum-Critical Dirac Semimetal
• Remarks on classical pseudo-electrodynamics
• Hubbard Model on the Honeycomb Lattice with an Indefinite Long-Range Interaction
• The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics
• Effective potential of scalar Lee-Wick pseudo-electrodynamics
• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion
• Charge density waves and stripes in quarter metals of graphene heterostructures
• Orthogonal Dirac semimetal on honeycomb lattice and the electron spectral function in orthogonal metallic states
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