Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.

Abstract

A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different directions.

12 pages, LaTeX (RevTeX 3.0)

Cited by in corpus (145)

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• Topological orders and Edge excitations in FQH states
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• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Fractional topological insulators
• Protected edge modes without symmetry
• Quantum Hall Physics - hierarchies and CFT techniques
• Fractional Quantum Hall Effect of Composite Fermions
• Classification and analysis of two dimensional abelian fractional topological insulators
• Theory of defects in Abelian topological states
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Edge excitations of paired fractional quantum Hall states
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Classification of Topological Defects in Abelian Topological States
• Wire deconstructionism of two-dimensional topological phases
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
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• Continuous topological phase transitions between clean quantum Hall states
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• Conformal invariance of chiral edge theories
• Fractional (Chern and topological) insulators
• Symmetric Mass Generation
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• In and around Abelian anyon models
• Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Comments on Symmetric Mass Generation in 2d and 4d
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Non-Perturbative Regularization of 1+1D Anomaly-Free Chiral Fermions and Bosons: On the equivalence of anomaly matching conditions and boundary gapping rules
• Classification of Disordered Phases of Quantum Hall Edge States
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
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• A Solution to the 1+1D Gauged Chiral Fermion Problem
• Wire constructions of Abelian topological phases in three or more dimensions
• CPT theorem and classification of topological insulators and superconductors
• Topological order in a correlated Chern insulator
• Topological Phase Transition in the $\nu =2/3$ Quantum Hall Effect
• Gapped Chiral Fermions
• Weak symmetry breaking in two dimensional topological insulators
• (Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• Critical points in edge tunneling between generic FQH states
• Second Generation of Composite Fermions in the Hamiltonian Theory
• Creating topological interfaces and detecting chiral edge modes in a 2D optical lattice
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• Corner states of topological fullerenes
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
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• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Correlation effects on topological crystalline insulators
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings
• Charge Excitations in Doped Mott Insulator in One Dimension
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• Parafermionic wires at the interface of chiral topological states
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
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• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Theory of the Quantum Hall Smectic Phase II: Microscopic Theory
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• Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry
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• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
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