Condensing non-Abelian quasiparticles

Abstract

A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differ from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at $\nu =4/3$ as an explicit example.

References in corpus (11)

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• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Quantum Hall system in Tao-Thouless limit
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• One-Dimensional Theory of the Quantum Hall System
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• Quantum Hall quasielectron operators in conformal field theory
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• Halperin (m, m',n) bilayer quantum Hall states on thin cylinders
• Quantum Hall quasielectrons - Abelian and non-Abelian
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Cited by in corpus (24)

• Quantum Hall Physics - hierarchies and CFT techniques
• Tunneling of anyonic Majorana excitations in topological superconductors
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Hall Viscosity of Hierarchical Quantum Hall States
• Unpaired composite fermion, topological exciton, and zero mode
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Tripartite Composite Fermion States
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Quasihole condensates in quantum Hall liquids
• Partition Functions of Non-Abelian Quantum Hall States
• Composite Fermion states on the torus
• A general approach to quantum Hall hierarchies
• One-dimensional itinerant interacting non-Abelian anyons
• Matrix product state representation of quasielectron wave functions
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions
• Non-Abelian phases from the condensation of Abelian anyons
• Braiding properties of paired spin-singlet and non-abelian hierarchy states
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Conformal field theory construction for nonabelian hierarchy wave functions
• Proliferation transitions from a topological phase in $2+1$ dimensions