Wess-Zumino-Witten Terms in Graphene Landau Levels

Abstract

We consider the interplay between the antiferromagnetic and Kekulé valence bond solid orderings in the zero energy Landau levels of neutral monolayer and bilayer graphene. We establish the presence of Wess-Zumino-Witten terms between these orders: this implies that their quantum fluctuations are described by the deconfined critical theories of quantum spin systems. We present implications for experiments, including the possible presence of excitonic superfluidity in bilayer graphene.

5 pages, 2 figures. Supplemental material added (v3)

References in corpus (22)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Fate of CP(N-1) fixed points with q-monopoles
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Electronic multicriticality in bilayer graphene
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• SO(5) symmetry in the quantum Hall effect in graphene
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly
• Charge 2e skyrmions in bilayer graphene
• Spin Symmetry of the Bilayer Graphene Groundstate
• Geometric phases and competing orders in two dimensions
• Deconfined criticality in bilayer graphene
• Spontaneous Layer Polarization and Conducting Domain Walls in the Quantum Hall Regime of Bilayer Graphene
• Conserved charges of order-parameter textures in Dirac systems

Cited by in corpus (24)

• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Even denominator fractional quantum Hall states at an isospin transition in monolayer graphene
• Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Realizing topological surface states in a lower-dimensional flat band
• Nodal band-off-diagonal superconductivity in twisted graphene superlattices
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Strong-Magnetic-Field Magnon Transport in Monolayer Graphene
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Deconfined critical point in a doped random quantum Heisenberg magnet
• Thermal Transport Signatures of Broken-Symmetry Phases in Graphene
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Electronic band gaps and transport properties in periodically alternating mono- and bi-layer graphene superlattices
• SU(3) and SU(4) singlet quantum Hall states at $\nu =2/3$
• Topological terms on topological defects: a quantum Monte Carlo study
• Spin and valley ordering of fractional quantum Hall states in monolayer graphene
• Two-component parton fractional quantum Hall state in graphene
• Competing Orders and Anomalies
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Fractionalized Fermi liquids and the cuprate phase diagram
• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment