Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

Abstract

We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν= 2/3 and single-component systems at ν= 8/3.

4 pages + refs

References in corpus (12)

• Condensate induced transitions between topologically ordered phases
• Fractional Quantum Hall States and Jack Polynomials
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• A theory of topological edges and domain walls
• Fractional Quantum Hall Effect in the Second Landau Level
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• One-Dimensional Theory of the Quantum Hall System
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States

Cited by in corpus (57)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Genons, twist defects, and projective non-Abelian braiding statistics
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Anyon condensation and its applications
• Fractional topological superconductors with fractionalized Majorana fermions
• Universal Quantum Computation with Metaplectic Anyons
• Boson Condensation in Topologically Ordered Quantum Liquids
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• Superconducting analogue of the parafermion fractional quantum Hall states
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Synthetic Topological Degeneracy by Anyon Condensation
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Unconventional Quantum Critical Points
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• Ising anyons with a string tension
• Phase transitions in Z_N gauge theory and twisted Z_N topological phases
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• The modular S-matrix as order parameter for topological phase transitions
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Condensate-induced transitions and critical spin chains
• Light-induced fractional quantum Hall phases in graphene
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Competing topological orders in three dimensions: X-cube versus toric code
• Josephson Coupled Moore-Read States
• No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids
• Phases and phase transitions in a $U(1)\times U(1)$ system with $\theta =2\pi /3$ mutual statistics
• Disorder-generated non-Abelions
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Deconfined quantum critical point lost in pressurized SrCu2(BO3)2
• Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Topological symmetry breaking: Domain walls and partial instability of chiral edges
• Quantum phase transitions in the $K$-layer Ising toric code
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• (3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Edge Theories for Anyon Condensation Phase Transitions
• Gauging Defects in Quantum Spin Systems
• Topological quantum compilation of metaplectic anyons based on the genetic optimized algorithms
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Dihedral twist liquid models from emergent Majorana fermions
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Boson-Lattice Construction for Anyon Models