Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states

Abstract

We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub the orbifold FQH states, of which the Z4 parafermion (Read-Rezayi) state is a special case. This provides an example in which Z2 electron fractionalization leads to non-Abelian topological phases. The naive "ideal" wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases, but instead lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern of zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fraction 8/3 and 12/5, and as a way to tune to non-Abelian states in double-layer or wide quantum wells.

25 pages

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Cited by in corpus (49)

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• Theory of defects in Abelian topological states
• Anyon condensation and its applications
• Fractional topological superconductors with fractionalized Majorana fermions
• A theory of 2+1D bosonic topological orders
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Phase transitions in topological lattice models via topological symmetry breaking
• Superconducting analogue of the parafermion fractional quantum Hall states
• A continuous transition between fractional quantum Hall and superfluid states
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• The structure of spinful quantum Hall states: a squeezing perspective
• Phase transitions in Z_N gauge theory and twisted Z_N topological phases
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• The modular S-matrix as order parameter for topological phase transitions
• Frustrated topological symmetry breaking: geometrical frustration and anyon condensation
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Josephson Coupled Moore-Read States
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• Topological symmetry breaking: Domain walls and partial instability of chiral edges
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Topologically protected flatness in chiral moiré heterostructures
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Gauging Defects in Quantum Spin Systems
• Dihedral twist liquid models from emergent Majorana fermions
• Anomalous Bilayer Quantum Hall Effect
• Permutation actions on modular tensor categories of topological multilayer phases