Edge excitations of paired fractional quantum Hall states

Abstract

The Hilbert spaces of the edge excitations of several ``paired'' fractional quantum Hall states, namely the Pfaffian, Haldane-Rezayi and 331 states, are constructed and the states at each angular momentum level are enumerated. The method is based on finding all the zero energy states for those Hamiltonians for which each of these known ground states is the exact, unique, zero-energy eigenstate of lowest angular momentum in the disk geometry. For each state, we find that, in addition to the usual bosonic charge-fluctuation excitations, there are fermionic edge excitations. The edge states can be built out of quantum fields that describe the fermions, in addition to the usual scalar bosons (or Luttinger liquids) that describe the charge fluctuations. The fermionic fields in the Pfaffian and 331 cases are a non-interacting Majorana (i.e., real Dirac) and Dirac field, respectively. For the Haldane-Rezayi state, the field is an anticommuting scalar. For this system we exhibit a chiral Lagrangian that has manifest SU(2) symmetry but breaks Lorentz invariance because of the breakdown of the spin statistics connection implied by the scalar nature of the field and the positive definite norm on the Hilbert space. Finally we consider systems on a cylinder where the fluid has two edges and construct the sectors of zero energy states, discuss the projection rules for combining states at the two edges, and calculate the partition function for each edge excitation system at finite temperature in the thermodynamic limit. It is pointed out that the conformal field theories for the edge states are examples of orbifold constructions.

44 pages, requires RevTeX, no figures

Cited by in corpus (145)

• Non-Abelian Anyons and Topological Quantum Computation
• 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
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Observation of neutral modes in the fractional quantum Hall regime
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Parafermion Hall states from coset projections of abelian conformal theories
• Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors
• Projective Construction of Non-Abelian Quantum Hall Liquids
• The non-Abelian Interferometer
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• On Fusion Rules in Logarithmic Conformal Field Theories
• Quantum Hall fractions for spinless Bosons
• Topological Entanglement Entropy from the Holographic Partition Function
• Modular Invariant Partition Functions in the Quantum Hall Effect
• The Haldane-Rezayi Quantum Hall State and Conformal Field Theory
• Conformal invariance of chiral edge theories
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Evaluation of ranks of real space and particle entanglement spectra for large systems
• Composite Dirac liquids: parent states for symmetric surface topological order
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Edge States and Interferometers in the Pfaffian and anti-Pfaffian States
• Entanglement spectra of complex paired superfluids
• The continuum limit of sl(N/K) integrable super spin chains
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Paired fractional quantum Hall states and the nu=5/2 puzzle
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State
• Striped quantum Hall state in a half-filled Landau level
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Topological Degeneracy of Quantum Hall Fluids
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Boundary Conformal Field Theory and Tunneling of Edge Quasiparticles in non-Abelian Topological States
• Relating c<0 and c>0 Conformal Field Theories
• Surface modes of ultracold atomic clouds with very large number of vortices
• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• The effects of non-abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Odd-Even Crossover in a non-Abelian $\nu =5/2$ Interferometer
• The structure of spinful quantum Hall states: a squeezing perspective
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Entangled Pauli Principles: the DNA of Quantum Hall Fluids
• Fractional Excitonic Insulator
• Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Quantum Hall hierarchy from coupled wires
• Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states
• Quantum Hall Bilayers and the Chiral Sine-Gordon Equation
• Composite Fermion Metals from Dyon Black Holes and S-Duality
• Edge excitations and Topological orders in rotating Bose gases
• Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Local two-body parent Hamiltonians for the entire Jain sequence
• Phase diagram and edge states of the $\nu =5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Light-induced fractional quantum Hall phases in graphene
• Construction of the edge states in fractional quantum Hall systems by Jack polynomial
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• Universality in Quantum Hall Systems: Coset Construction of Incompressible States
• A conformal field theory description of the paired and parafermionic states in the quantum Hall effect
• Universal entanglement spectra in critical spin chains
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Meron deconfinement in the quantum Hall bilayer at intermediate distances
• Generalized Tambara-Yamagami categories
• A Matrix Model for WZW
• The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Three-body correlations and finite-size effects in the Moore--Read states on a sphere
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• Josephson Coupled Moore-Read States
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories
• Pairing Effects in the Edge of Paired Quantum Hall States
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Modular Invariants in the Fractional Quantum Hall Effect
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• The Haldane-Rezayi Quantum Hall State and Magnetic Flux
• Distinguishing particle-hole conjugated Fractional Quantum Hall states using quantum dot mediated edge transport
• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Aharonov-Bohm effect in the non-Abelian quantum Hall fluid
• Non-Abelian fractional quantum Hall states and chiral coset conformal field theories
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• A Novel CFT Approach to Bulk Wave Functions in the Fractional Quantum Hall Effect
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories
• Invariant structure of the hierarchy theory of fractional quantum Hall states with spin
• Persistent edge currents for paired quantum hall states
• Holographic Chern-Simons Defects
• Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases
• Edge-Induced Qubit Polarization in Systems with Ising Anyons
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Spin-singlet hierarchy in the fractional quantum Hall effect
• Tunneling in Paired Fractional Quantum Hall States: Conductance and Andreev Reflection of Non-Abelions
• In-plane electric fields and the $\nu =\frac{5}{2}$ fractional quantum Hall effect in a disk geometry
• Field theory of spin-singlet quantum Hall states
• Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields
• Dynamics of Quantum Hall Interfaces
• Identification of the Fractional quantum Hall edge modes by density oscillations
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom
• Point-like topological defects in bilayer quantum Hall systems
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• The edge theory of ferromagnetic quantum Hall states
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Electron and Quasiparticle Exponents of Haldane-Rezayi state in Non-abelian Fractional Quantum Hall Theory
• Stability and Activation Gaps of Parafermionic Hall States in the Second Landau Level
• Strong quasi-particle tunneling study in the paired quantum Hall states
• Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State
• Andreev-like Reflection in the Pfaffian Fractional Quantum Hall Effect
• PH Pfaffian intra and inter correlations in the quantum Hall bilayer
• Supersymmetric Hamiltonian Approach to Edge Excitations in $\nu =5/2$ Fractional Quantum Hall Effect
• Gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (Non-Abelian) Chern-Simon theory
• Paired quantum Hall states on noncommutative two-tori
• Dynamics of edge Majorana fermions in $\nu =\frac{5}{2}$ fractional quantum Hall effects
• Computational equivalence of the two inequivalent spinor representations of the braid group in the Ising topological quantum computer
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Pairing symmetry transitions in the even-denominator FQHE system
• Multiple Edge Partition Functions For Fractional Quantum Hall States
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states
• Boundary critical phenomena in the quantum Ashkin-Teller model