Collective states of non-abelian quasiparticles in a magnetic field

Abstract

Motivated by the physics of the Moore-Read ν= 1/2 state away from half-filling, we investigate collective states of non-abelian e/4 quasiparticles in a magnetic field. We consider two types of collective states: incompressible liquids and Wigner crystals. In the incompressible liquid case, we construct a natural series of states which can be thought of as a non-abelian generalization of the Laughlin states. These states are associated with a series of hierarchical states derived from the Moore-Read state - the simplest of which occur at filling fraction 8/17 and 7/13. Interestingly, we find that the hierarchical states are abelian even though their parent state is non-abelian. In the Wigner crystal case, we construct two candidate states. We find that they, too, are abelian - in agreement with previous analysis.

11 pages

References in corpus (5)

• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Interacting anyons in topological quantum liquids: The golden chain
• Fractional Quantum Hall Hierarchy and the Second Landau Level

Cited by in corpus (35)

• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• Quantum Hall Physics - hierarchies and CFT techniques
• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Tunneling of anyonic Majorana excitations in topological superconductors
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Majorana fermions in vortex lattices
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Energetics of Pfaffian-AntiPfaffian Domains
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Condensing non-Abelian quasiparticles
• Quantum Hall hierarchy from coupled wires
• Composite-fermion pairing at half and quarter filled lowest Landau level
• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Matrix product state representation of quasielectron wave functions
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• 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
• Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Ordering the topological order in the fractional quantum Hall effect
• Conformal field theory construction for nonabelian hierarchy wave functions
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Non-Abelian phases from the condensation of Abelian anyons
• Proliferation transitions from a topological phase in $2+1$ dimensions
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures