Quantum Hall quasielectron operators in conformal field theory

Abstract

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.

minor changes, published

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Cited by in corpus (38)

• Quantum Hall Physics - hierarchies and CFT techniques
• Exact Matrix Product States for Quantum Hall Wave Functions
• Unpaired composite fermion, topological exciton, and zero mode
• Geometric construction of Quantum Hall clustering Hamiltonians
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• The structure of spinful quantum Hall states: a squeezing perspective
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Tripartite Composite Fermion States
• Condensing non-Abelian quasiparticles
• Composite Fermions on a Torus
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Quasihole condensates in quantum Hall liquids
• Partition Functions of Non-Abelian Quantum Hall States
• Composite Fermion states on the torus
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• The quantum Hall hierarchy in spherical geometry
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• A general approach to quantum Hall hierarchies
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Optical control over bulk excitations in fractional quantum Hall systems
• Laughlin states and their quasi-particle excitations on the torus
• Charge Fractionalization on Quantum Hall Edges
• Matrix product state representation of quasielectron wave functions
• Microscopic study of the 2/5 fractional quantum Hall edge
• Hierarchical Nature of the Quantum Hall Effects
• Quasielectrons in lattice Moore-Read models
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect
• Continuum limit of lattice quasielectron wavefunctions
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
• Conformal field theory construction for nonabelian hierarchy wave functions
• Non-Abelian phases from the condensation of Abelian anyons
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• Particle-Hole Mirror Symmetries around the Half-Filled Shell: The Quantum Numbers and Algebraic Structure of Composite Fermions
• Proposal for bulk measurement of braid statistics in fractional quantum Hall effect
• Minimal Models for a Superconductor-Insulator Conformal Quantum Phase Transition