Parafermion Hall states from coset projections of abelian conformal theories

Abstract

The Z_k-parafermion Hall state is an incompressible fluid of k-electron clusters generalizing the Pfaffian state of paired electrons. Extending our earlier analysis of the Pfaffian, we introduce two ``parent'' abelian Hall states which reduce to the parafermion state by projecting out some neutral degrees of freedom. The first abelian state is a generalized (331) state which describes clustering of k distinguishable electrons and reproduces the parafermion state upon symmetrization over the electron coordinates. This description yields simple expressions for the quasi-particle wave functions of the parafermion state. The second abelian state is realized by a conformal theory with a (2k-1)-dimensional chiral charge lattice and it reduces to the Z_k-parafermion state via the coset construction su(k)_1+su(k)_1/su(k)_2. The detailed study of this construction provides us a complete account of the excitations of the parafermion Hall state, including the field identifications, the Z_k symmetry and the partition function.

Latex, 36 pages, 3 tables, 2 figures

References in corpus (10)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• A Unified Conformal Field Theory Description of Paired Quantum Hall States
• Parafermion Statistics and Quasihole Excitations for the Generalizations of the Paired Quantum Hall States
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Universality in Quantum Hall Systems: Coset Construction of Incompressible States

Cited by in corpus (104)

• Non-Abelian Anyons and Topological Quantum Computation
• Rapidly Rotating Atomic Gases
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Anyons and the quantum Hall effect - a pedagogical review
• Quantum Hall Physics - hierarchies and CFT techniques
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Quantum groups and nonabelian braiding in quantum Hall systems
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Quantum Hall physics in rotating Bose-Einstein condensates
• Generalized Quantum Hall Projection Hamiltonians
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Quantum Hall states and boson triplet condensate for rotating spin-1 bosons
• Wavefunctions for topological quantum registers
• Rotating spin-1 bosons in the lowest Landau level
• Quantum Hall quasielectron operators in conformal field theory
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Local exclusion principle for identical particles obeying intermediate and fractional statistics
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• The structure of spinful quantum Hall states: a squeezing perspective
• Coulomb Blockade Doppelgangers in Quantum Hall States
• Tripartite Composite Fermion States
• Filling the Bose sea: symmetric quantum Hall edge states and affine characters
• Condensing non-Abelian quasiparticles
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Parafermion statistics and the application to non-abelian quantum Hall states
• A Matrix Model for Non-Abelian Quantum Hall States
• Many-anyon trial states
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• Parafermionic states in rotating Bose-Einstein condensates
• Quasihole condensates in quantum Hall liquids
• Partition Functions of Non-Abelian Quantum Hall States
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• A general approach to quantum Hall hierarchies
• Canonical quantization of the boundary Wess-Zumino-Witten model
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states
• Chiral Partition Functions of Quantum Hall Droplets
• Fractional quantum Hall effect in a U(1)xSU(2) gauge field
• Partition Functions and Stability Criteria of Topological Insulators
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge
• Constructing topological models by symmetrization: A PEPS study
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Deconfinement at N>2: SU(N) Georgi-Glashow model in 2+1 dimensions
• Twisted Parafermions
• Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases
• Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Correlators of N=1 Superconformal Currents
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Properties of 2D anyon gas
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• K-matrices for 2D conformal field theories
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Charged spin textures over the Moore-Read quantum Hall state
• Coset Vertex Operator Algebras and $\W$-Algebras
• Stability and Activation Gaps of Parafermionic Hall States in the Second Landau Level
• Reply to "Comment on `Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength' "
• Exchange and exclusion in the non-abelian anyon gas
• Characterizing Topological Order in Superconducting Systems
• Braiding Fibonacci anyons
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Non-Abelian phases from the condensation of Abelian anyons
• Conformal field theory construction for nonabelian hierarchy wave functions
• Emergent Supersymmetry on the Edges
• Quantum dimensions and fusion rules for parafermion vertex operator algebras
• Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Level-Rank Duality for Vertex Operator Algebras of types B and D
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Thermoelectric characteristics of ${\mathbb{Z}}_k$ parafermion Coulomb islands
• W-algebras related to parafermion algebras
• Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect
• Exact modular $S$ matrix for the ${\mathbb{Z}}_k$ parafermion quantum Hall islands and measurement of non-Abelian anyons
• Spin texture readout of a Moore-Read topological quantum register
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states