Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level

Abstract

The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions, for all integers k > 0. The remarkably simple wavefunctions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The k=2 case is the Pfaffian. For k > 1, the quasiparticle excitations of these systems are expected to possess nonabelian statistics, like those of the Pfaffian. For k=3, these ground states have large overlaps with the ground states of the (2-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors ν=2+3/5, 2+2/5.

11 pages Revtex in two column format with 4 eps figures included in the MS

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• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• Scrambling via Braiding of Nonabelions
• Supersymmetry in the Fractional Quantum Hall Regime
• Energy projection and modified Laughlin states
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Pair-distribution functions of correlated composite fermions
• Non-abelian quantum Hall states - exclusion statistics, K-matrices and duality
• Highest weight Macdonald and Jack Polynomials
• Bosonic integer quantum Hall effect as topological pumping
• Fractionalization of itinerant anyons in one dimensional chains
• Fractional quantum Hall states of a Bose gas with spin-orbit coupling
• Effect of Landau Level Mixing on Braiding Statistics
• Laughlin states and their quasi-particle excitations on the torus
• Constructing topological models by symmetrization: A PEPS study
• Theory of vortex-lattice melting in a one-dimensional optical lattice
• Engineering Yang-Lee anyons via Majorana bound states
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Universal Periods in Quantum Hall Droplets
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• Geometric responses of the Pfaffian state
• Systematically generated two-qubit anyon braids
• Functional completeness of planar Rydberg blockade structures
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• A Typology for Quantum Hall Liquids
• Identifying non-Abelian topological ordered state and transition by momentum polarization
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Topological phase, supercritical point and emergent phenomena in extended ${\mathbb{Z}}_3$ parafermion chain
• Bosonization for fermions and parafermions
• Measures of entanglement in non-Abelian anyonic systems
• Universal quantum computing with parafermions assisted by a half fluxon
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Exploiting Geometric Degrees of Freedom in Topological Quantum Computing
• Disorder-generated non-Abelions
• Local density of states and particle entanglement in topological quantum fluids
• Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
• SU(3) and SU(4) singlet quantum Hall states at $\nu =2/3$
• Universal topological quantum computation with strongly correlated Majorana edge modes
• Compass and Kitaev models -- Theory and Physical Motivations
• Parafermion excitations in superfluid of quasi-molecular chains
• Elementary Excitations in Fractional Quantum Hall Effect from Classical Constraints
• A Temperley-Lieb quantum chain with two- and three-site interactions
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Fractional domain walls from on-site softening in dipolar bosons
• Simulation of braiding anyons using Matrix Product States
• Automatic design of Hamiltonians
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Spin chain description of rotating bosons at $\nu =1$
• ${\mathbf{Z}}_n$ clock models and chains of $so(n{)}_2$ non-Abelian anyons: symmetries, integrable points and low energy properties
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• Topological Quantum Gate Construction by Iterative Pseudogroup Hashing
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms
• Aharonov-Bohm effect in the non-Abelian quantum Hall fluid
• Non-Abelian fractional quantum Hall states and chiral coset conformal field theories
• Gaffnian holonomy through the coherent state method
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Topological invariants for the fractional quantum Hall states
• Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System
• Identifying non-Abelian anyons with upstream noise
• Gauging U(1) symmetry in (2+1)d topological phases
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Gapped Boundary Phases of Topological Insulators via Weak Coupling
• Do Rydberg chains yield Fibonacci anyons?
• Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories
• Quantum Hall Circle
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases
• Effective models of doped quantum ladders of non-Abelian anyons
• Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories
• M${}_k$ models: the field theory connection
• Observation of 1/3 fractional quantum Hall physics in balanced large angle twisted bilayer graphene
• On the Structure of Edge State Inner Products in the Fractional Quantum Hall Effect
• Parafermions in Hierarchical Fractional Quantum Hall States
• Generalizations of Perelomov's identity on the completeness of coherent states
• Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules
• Paired parton quantum Hall states: a coupled wire construction
• Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions
• Elaborating the phase diagram of spin-1 anyonic chains
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• A many-body Fredholm index for ground state spaces and Abelian anyons
• Dynamical topological excitations in parafermion chains
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• Fractional quantum Hall effect from frustration-free Hamiltonians
• Composite anyon coding and the initialization of a topological quantum computer
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Generalized Gibbs Ensemble Description of Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems with $SU(2)$ Symmetry
• Unified Fock space representation of fractional quantum Hall states
• Tunnelling current through fractional quantum Hall interferometers
• Heat equation approach to geometric changes of the torus Laughlin-state
• Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
• Classification of topological symmetry sectors on anyon rings
• Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux
• Non-Abelian $SU(3{)}_k$ anyons: inversion identities for higher rank face models
• Numerical simulation of non-abelian anyons
• Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases
• Dynamics of Rapidly Rotating Bose-Einstein Quantum Droplets
• Topological entanglement entropy in the second Landau level
• Paths and partitions: combinatorial descriptions of the parafermionic states
• A magnetic model with a possible Chern-Simons phase
• Quantum dots as parafermion detectors
• Vector valued Macdonald polynomials
• Dynamic mass generation and topological order in overscreened Kondo lattices
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields
• Effect of inter-edge Coulomb interactions on transport through a point contact in a ν= 5/2 quantum Hall state
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• FQHE and $t{t}^{\ast }$ geometry
• Identification of the Fractional quantum Hall edge modes by density oscillations
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Deterministic quantum one-time pad via Fibonacci anyons
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• From Composite Fermions to Calogero-Sutherland Model: Edge of Fractional Quantum Hall Liquid and the Dimension Reduction
• Defects and degeneracies in supersymmetry protected phases
• A numerical study of bounds in the correlations of fractional quantum Hall states
• Geometric bound on structure factor
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Pfaffian States in Coupled Atom-Cavity Systems
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Phase transitions on a ladder of braided non-Abelian anyons
• Charge density waves and their transitions in anisotropic quantum Hall systems
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Spinless basis for spin-singlet FQH states
• Edge ${\mathbb{Z}}_3$ parafermions in fermionic lattices
• (3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases
• Ternary Logic Design in Topological Quantum Computing
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Correlators of N=1 Superconformal Currents
• Properties of 2D anyon gas
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Parafermions in Moiré Minibands
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Chern-Simons theory of multi-component quantum Hall systems
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topologization of electron liquids with Chern-Simons theory and quantum computation
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Geometry and large N limits in Laughlin states
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• K-matrices for 2D conformal field theories
• An anyon model in a toric honeycomb lattice
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Numerical studies of the fractional quantum Hall effect in systems with tunable interactions
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Renormalization group flows for $Z_5$ parafermionic field theory
• Kinetic formation of trimers in a spinless fermionic chain
• Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect
• Hyperdeterminantal computation for the Laughlin wave function
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• On the particle entanglement spectrum of the Laughlin states
• Fractional quantum Hall states of dipolar fermions in a strained optical lattice
• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
• Collective excitations of quantum Hall states under tilted magnetic field
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
• Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Renormalization group flows for the second $Z_N$ parafermionic field theory for N odd
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Stability and Activation Gaps of Parafermionic Hall States in the Second Landau Level
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Exchange and exclusion in the non-abelian anyon gas
• Dihedral twist liquid models from emergent Majorana fermions
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Detecting Hidden Order in Fractional Chern Insulators
• A Parafermionic Generalization of the Jaynes Cummings Model
• Anyonic quasiparticles of hardcore anyons
• A non-invasive method for nanoscale electrostatic gating of pristine materials
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Thermodynamics of non-abelian exclusion statistics
• Partial fillings of the bosonic $E_8$ quantum Hall state
• Topological ground state degeneracy of the two-channel Kondo lattice
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Non-Abelian phases from the condensation of Abelian anyons
• Exciton fractional Chern insulators in moiré heterostructures
• Iterants, Idempotents and Clifford algebra in Quantum Theory
• Ordering the topological order in the fractional quantum Hall effect
• Determination of many-electron basis functions for a Quantum Hall ground state using Schur polynomials
• Spinon bases in supersymmetric CFTs
• Linear dependencies between Composite Fermion states
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Emergent Supersymmetry on the Edges
• Conformal field theory construction for nonabelian hierarchy wave functions
• Anyon Chains with Pairing Terms
• Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• A probabilistic evolutionary optimization approach to compute quasiparticle braids
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Correlations in lowest Landau level vortex states
• Universal properties of the FQH state from the topological entanglement entropy and disorder effects
• Quasiparticle agglomerates in Read-Rezayi and anti Read-Rezayi state
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Composite fermion basis for two-component Bose gases
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level
• Even-denominator fractional quantum Hall states with spontaneously broken rotational symmetry
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Symmetry-Protected Local Minima in Infinite DMRG
• Chiral Edge States Emerging on Anyon-Net
• Liouville perturbation theory for Laughlin state and Coulomb gas
• Giga fine-structure constant in photonic solitons
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Quantum impurity models from conformal field theory
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures
• Topological Protection in a Landau Flat Band at $\nu =7/11$, a Candidate Filling Factor for Unconventional Correlations
• Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect
• New type of solutions of Yang-Baxter equations, quantum entanglement and related physical models
• Cascade of fractional quantum Hall states in 2D system
• Exact modular $S$ matrix for the ${\mathbb{Z}}_k$ parafermion quantum Hall islands and measurement of non-Abelian anyons
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• Second-quantized approach to the study of Halperin state in fractional quantum Hall effect
• Fractional Quantum Hall Effects in HgTe Quantum Wells
• Search for electron liquids with non-Abelian quasiparticles
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Almost linear Haldane pseudopotentials and emergent conformal block wave-functions in a Landau level
• Effective mass of composite fermion: a phenomenological fit in with anomalous propagation of surface acoustic wave
• Boson-Lattice Construction for Anyon Models
• Condensates of interacting non-Abelian $SO(5{)}_{N_f}$ anyons
• Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
• Exact Mappings in Condensed Matter Physics
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states
• Radiative neutrino mass models from non-invertible selection rules
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state
• Fermionization, Triangularization and Integrability
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Cotunneling in the ν= 5/2 fractional quantum Hall regime
• $t{t}^{\ast }$ Geometry of Modular Curves
• Hyperspherical Slater determinant approach to few-body fractional quantum Hall states
• Composite fermion basis for M-component Bose gases
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model
• Orbital Description of Landau Levels