Topological spin ordering via Chern-Simons superconductivity

Abstract

We use the Chern-Simons (CS) fermion representation of s =1/2 spin operators to construct topological, long-range magnetically ordered states of interacting two-dimensional (2D) quantum spin models. We show that the fermion-fermion interactions mediated by the dynamic CS flux attachment may give rise to Cooper pairing of the fermions. Specifically, in an XY model on the honeycomb lattice, this construction leads to a "CS superconductor," which belongs to a topologically non-trivial in 2D symmetry class DIII, with particle-hole and time-reversal symmetries. It is shown that in the original spin language, this state corresponds to a symmetry protected topological state, which coexists with a magnetic long-range order. We discuss physical manifestations of the topological character of the corresponding state and requirements for models that could host it.

Main text: 5 pages, 2 figures. Supplement: 2 pages, 1 figure

References in corpus (42)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Quantum Spin Liquids
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Quantum Orders and Symmetric Spin Liquids
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Quantum magnetism and criticality
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Fermion zero modes on vortices in chiral superconductors
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Unusual ordered phases of highly frustrated magnets: a review
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• On edge states in superconductor with time inversion symmetry breaking
• The half-filled Landau level: the case for Dirac composite fermions
• Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Mutual Chern-Simons theory for Z_2 topological order
• Composite fermion state of spin-orbit coupled bosons
• Bott periodicity for $Z_2$ symmetric ground states of gapped free-fermion systems
• Spin Induced Optical Conductivity in the Spin Liquid Candidate Herbertsmithite
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: Scenario for Cs_2CuCl_4
• Absence of Bose condensation on lattices with moat bands
• Statistical transmutation in Floquet driven optical lattices
• Synthetic gauge fields stabilize a chiral spin liquid phase
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• Quantum spin liquids and the metal-insulator transition in doped semiconductors

Cited by in corpus (21)

• Non-local topological electromagnetic phases of matter
• Fermionization of Bosons in a Flat Band
• Theory of competing Chern-Simons orders and emergent phase transitions
• Chern-Simons superconductors and their instabilities
• Antiferromagnetic magnons from fractionalized excitations
• Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction
• Phase diagrams of Bose-Hubbard model and antiferromagnetic spin-1/2 models on a honeycomb lattice
• Chiral spin liquid state of strongly interacting bosons with a moat dispersion: a Monte Carlo simulation
• Helical spin liquid in a triangular XXZ magnet from Chern-Simons theory
• Emergent Kondo behavior from gauge fluctuations in spin liquids
• Topologically enabled superconductivity
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Simplified Two-Dimensional Model for Global Atmospheric Dynamics
• Jordan-Wigner fermionization of quantum spin systems on arbitrary 2D lattices: A mutual Chern-Simons approach
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Chern-Simons approach to atmospheric dynamics
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model
• Quantization and quantum oscillations of the sublattice charge order in Dirac insulators
• Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian