Geometric phases and competing orders in two dimensions

Abstract

We discuss the problem of characterizing "quantum disordered" ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response in electron bilinears to the skyrmion density in the local antiferromagnetic order, induced by geometric phases. We also discuss the connection to topological terms obtained under situations where the electronic spectrum has a Dirac form.

36 pages, 5 figures

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• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• Impurity spin texture at a deconfined quantum critical point
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Cited by in corpus (22)

• Gauge theory for the cuprates near optimal doping
• The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals
• The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity
• Wess-Zumino-Witten Terms in Graphene Landau Levels
• Spin density wave order, topological order, and Fermi surface reconstruction
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Phase diagram of the strongly correlated Kane-Mele-Hubbard model
• The landscape of the Hubbard model
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Symmetry Analysis of Holes Localized on a Skyrmion in a Doped Antiferromagnet
• Deconfined criticality in bilayer graphene
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
• Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice
• Competing Orders and Anomalies
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Holes Localized on a Skyrmion in a Doped Antiferromagnet on the Honeycomb Lattice: Symmetry Analysis
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Interplay between interaction and chiral anomaly in the holographic approach
• Topological quantum control: Edge currents via Floquet depinning of skyrmions in the $\nu =0$ graphene quantum Hall antiferromagnet
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions