From Luttinger liquid to non-Abelian quantum Hall states

Abstract

We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization provides a simple framework for characterizing the Moore Read state, as well as the more general Read Rezayi sequence. This coupled wire construction provides a solvable Hamiltonian formulated in terms of electronic degrees of freedom, and provides a direct route to characterizing the quasiparticles and edge states in terms of conformal field theory. This construction leads to a simple interpretation of the coset construction of conformal field theory, which is a powerful method for describing non Abelian states. In the present context, the coset construction arises when the original chiral modes are fractionalized into coset sectors, and the different sectors acquire energy gaps due to coupling in "different directions". The coupled wire construction can also can be used to describe anisotropic lattice systems, and provides a starting point for models of fractional and non-Abelian Chern insulators. This paper also includes an extended introduction to the coupled wire construction for Abelian quantum Hall states, which was introduced earlier.

23 pages, 10 figures

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Fractional quantum Hall states at zero magnetic field
• Fractional quantum Hall effect in the absence of Landau levels
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Fractional topological insulators in three dimensions
• A short introduction to Fibonacci anyon models
• Quantum Hall system in Tao-Thouless limit
• Fractional Quantum Hall Hierarchy and 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
• Topological Quantum Compiling
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Non-Abelian Braiding of Lattice Bosons
• Fractional Chern Insulators from the nth Root of Bandstructure
• Nature of the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model

Cited by in corpus (214)

• Colloquium: Topological Band Theory
• Theory of Intertwined Orders in High Temperature Superconductors
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Interacting topological insulators: a review
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Topological phases with parafermions: theory and blueprints
• Nonlinearity-induced photonic topological insulator
• Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Wire deconstructionism of two-dimensional topological phases
• Free parafermions
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Topological Floquet Phases in Driven Coupled Rashba Nanowires
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Parafermions in Interacting Nanowire Bundle
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Band structure engineering of ideal fractional Chern insulators
• Coupled wire construction of chiral spin liquids
• Magnetic crystals and helical liquids in alkaline-earth fermionic gases
• Superconducting analogue of the parafermion fractional quantum Hall states
• Proximity-induced Josephson $\pi$-Junctions in Topological Insulators
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Non-Abelian topological insulators from an array of quantum wires
• Majorana Fermions in Ge/Si Hole Nanowires
• Chiral Spin Liquids in Arrays of Spin Chains
• Layer construction of 3D topological states and string braiding statistics
• Quantum Spin Hall Effect in Strip of Stripes Model
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Composite Dirac liquids: parent states for symmetric surface topological order
• Pairing in Luttinger Liquids and Quantum Hall States
• Chiral currents in one-dimensional fractional quantum Hall states
• Fractional Topological Superconductivity and Parafermion Corner States
• Fractional Topological Insulators -- a Pedagogical Review
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Fractional Charge and Spin States in Topological Insulator Constrictions
• Precursor of Laughlin state of hard core bosons on a two leg ladder
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Integer and Fractional Quantum Hall Effect in a Strip of Stripes
• Driven dissipative dynamics and topology of quantum impurity systems
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Criticality in Translation-Invariant Parafermion Chains
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Generalized Kitaev Models and Slave Genons
• Fibonacci Topological Superconductor
• Wire constructions of Abelian topological phases in three or more dimensions
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Fractional topological phases in three-dimensional coupled-wire systems
• From an array of quantum wires to three-dimensional fractional topological insulators
• On the Holographic Dual of a Topological Symmetry Operator
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Microscopic characterization of Ising conformal field theory in Rydberg chains
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Lattice spin models for non-Abelian Chiral Spin Liquids
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Pretopological fractional excitations in the two-leg flux ladder
• Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• From fractional boundary charges to quantized Hall conductance
• Photon echo from lensing of fractional excitations in Tomonaga-Luttinger spin liquid
• Quantum Hall hierarchy from coupled wires
• Fractional chiral superconductors
• Coupled Atomic Wires in a Synthetic Magnetic Field
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Systematic construction of topological flat-band models by molecular-orbital representation
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Quadrupole spin polarization as signature of second-order topological superconductors
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Evidence for Two Dimensional Anisotropic Luttinger Liquids at Millikelvin Temperatures
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• A model of chiral spin liquids with Abelian and non-Abelian topological phases
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Hidden spin current in doped Mott antiferromagnets
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Non-diagonal anisotropic quantum Hall states
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Coupled wire construction of a topological phase with chiral tricritical Ising edge modes
• From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Symmetry-protected non-Fermi liquids, Kagome spin liquids, and the chiral Kondo lattice model
• Coupled Wire Model of Z4 Orbifold Quantum Hall States
• Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders
• A non-Abelian twist to integer quantum Hall states
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• Lattice Clifford fractons and their Chern-Simons-like theory
• Emergent mode and bound states in single-component one-dimensional lattice fermionic systems
• Josephson Coupled Moore-Read States
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
• Supersymmetry in the Fractional Quantum Hall Regime
• Classification and construction of interacting fractonic higher-order topological phases
• The resonant state at filling factor ν = 1/2 in chiral fermionic ladders
• Fractonic topological phases from coupled wires
• General scatterings and electronic states in the quantum-wire network of moiré systems
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• $Z_3$ generalization of the Kitaev's spin-1/2 model
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Local impurity in multichannel Luttinger liquid
• Electrically tunable correlated domain wall network in twisted bilayer graphene
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Tunneling Spectroscopy of Quantum Hall States in Bilayer Graphene PN Networks
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Composite helical edges from Abelian fractional topological insulators
• Crystallization of fractional charges in a strongly interacting quasi-helical quantum dot
• Exploring helical phases of matter in bosonic ladders
• Coupled Wire Model of $Z_2\times Z_2$ Orbifold Quantum Hall States
• Persistence of gaps in the interacting Hofstadter model
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Chiral and Non-Chiral Edge States in Quantum Hall Systems with Charge Density Modulation
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• From Coupled Rashba Electron and Hole Gas Layers to 3D Topological Insulators
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study
• Generalized parafermions and non-local Josephson effect in multi-layer systems
• Quantum criticality in many-body parafermion chains
• Anyonic Liquids in Nearly Saturated Spin Chains
• Paired parton quantum Hall states: a coupled wire construction
• Parafermions in Hierarchical Fractional Quantum Hall States
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Bulk Pumping in 2D Topological Phases
• Duality between 3D Massive Thirring and Maxwell Chern-Simons models from 2D bosonization
• Network construction of non-Abelian chiral spin liquids
• Photo-induced SU(3) topological material of spinless fermions
• Giant anisotropic band flattening in twisted $\Gamma$ valley semiconductor bilayers
• Twisted coupled wire model for a moiré sliding Luttinger liquid
• Berezinskii-Kosteriltz-Thouless transition in disordered multi-channel Luttinger liquids
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Fermi Surface Resonance and Quantum Criticality in Strongly Interacting Fermi Gases
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Model of spin liquids with and without time-reversal symmetry
• Metal-insulator transition in a sliding Luttinger liquid with line defects
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Chern-Simons-Higgs transitions out of Topological Superconducting Phases
• Quantum Electronic Circuits for Multicritical Ising Models
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Artificial gauge fields in the t-z mapping for optical pulses: spatio-temporal wavepacket control and quantum Hall physics
• Effective Theories for 2+1 Dimensional Non-Abelian Topological Spin Liquids
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Dimensional reduction of Kitaev spin liquid at quantum criticality
• A coupled wire description of surface $ADE$ topological orders
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Floquet Flux Attachment in Cold Atomic Systems
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• The Detection of Unconventional Quantum Oscillations in Insulating 2D Materials
• Topological states constructed by two different trivial quantum wires
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Dihedral twist liquid models from emergent Majorana fermions
• Dimensional reduction of the Luttinger-Ward functional for spin-degenerate $D$-dimensional electron gases
• Microscopic theory of fractional excitations in gapless bilayer quantum Hall states: semi-quantized quantum Hall states
• Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description
• Topological ground state degeneracy of the two-channel Kondo lattice
• Designing (higher) Hall crystals
• Topological Dipole Insulator
• $G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains
• Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
• Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators
• Partial fillings of the bosonic $E_8$ quantum Hall state
• Fibonacci topological phase in arrays of anyonic chains
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders
• Chiral Edge States Emerging on Anyon-Net
• Fractional spin excitations and conductance in the spiral staircase Heisenberg ladder
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges
• Quantum criticality and confinement in weak Mott insulators
• Coupled-wire descriptions of unconventional quantum states in twisted nanostructures
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems
• Emergent electronic insulating states in a one-dimensional moiré superlattice
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Chiral Edge States in 2+1 Dimensional Topological Phases
• Spin-charge separation in two dimensions: spinon-chargon gauge theories from duality
• Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires