Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene

Abstract

We study the phase diagram of an effective model of competing nematic and antiferromagnetic orders of interacting electrons on the Bernal-stacked honeycomb bilayer, as relevant for bilayer graphene. In the noninteracting limit, the model features a semimetallic ground state with quadratic band touching points at the Fermi level. Taking the effects of short-range interactions into account, we demonstrate the existence of an extended region in the mean-field phase diagram characterized by coexisting nematic and antiferromagnetic orders. By means of a renormalization group approach, we reveal that the quantum phase transition from nematic to coexistent nematic-antiferromagnetic orders is continuous and characterized by emergent Lorentz symmetry. It falls into the $(2+1)$-dimensional relativistic Gross-Neveu-Heisenberg quantum universality class, which has recently been much investigated in the context of interacting Dirac systems in two spatial dimensions. The coexistence-to-antiferromagnetic transition, by contrast, turns out to be weakly first order as a consequence of the absence of continuous spatial rotational symmetry on the honeycomb bilayer. Implications for experiments in bilayer graphene are discussed.

arXiv comment18 pages, 5 figures, 1 table; v2: corrected typos and minor improvements, extended analysis of emergent Lorentz symmetry in four-fermion theory, published version

References in corpus (68)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Optimised Renormalisation Group Flows
• The nonperturbative functional renormalization group and its applications
• Strength of effective Coulomb interactions in graphene and graphite
• Interactions and phase transitions on graphene's honeycomb lattice
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene
• Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
• Broken symmetry states and divergent resistance in suspended bilayer graphene
• Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
• Theory of interacting electrons on the honeycomb lattice
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Many-body instability of Coulomb interacting bilayer graphene: RG approach
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Spontaneous symmetry breaking and Lifshitz transition in bilayer graphene
• Electron-electron interactions in graphene bilayers
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Spontaneously gapped ground state in suspended bilayer graphene
• Four - Fermi Theories in Fewer Than Four Dimensions
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Lattice Theory of Pseudospin Ferromagnetism in Bilayer Graphene: Competing Orders and Interaction Induced Quantum Hall States
• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Electronic multicriticality in bilayer graphene
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching
• Instabilities of interacting electrons on the honeycomb bilayer
• Antiferromagnetism in the Hubbard Model on the Bernal-stacked Honeycomb Bilayer
• Antiferromagnetic state in bilayer graphene
• Critical behavior of Dirac fermions from perturbative renormalization
• UV fixed-point structure of the three-dimensional Thirring model
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Critical behavior of the (2+1)-dimensional Thirring model
• Renormalization group analysis of quantum critical points in d-wave superconductors
• Interaction induced Dirac fermions from quadratic band touching in bilayer graphene
• Transport Gap in Suspended Bilayer Graphene at Zero Magnetic Field
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Regularization and supersymmetry-restoring counterterms in supersymmetric QCD
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Mott multicriticality of Dirac electrons in graphene
• Competing nodal d-wave superconductivity and antiferromagnetism
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Coexistence and competition of nematic and gapped states in bilayer graphene
• Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Quantifying the fragility of unprotected quadratic band crossing points
• Influence of hopping selfenergy and quasiparticle degradation on the antiferromagnetic ordering in the bilayer honeycomb Hubbard model

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• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
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• Twist-tuned quantum criticality in moiré bilayer graphene
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Quantum field theories of relativistic Luttinger fermions
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates
• Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions