Ordering the topological order in the fractional quantum Hall effect
arXiv:2505.14767 · doi:10.1103/7gtq-y9d9
Abstract
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.
83 pages, 4 figures, 2 tables; updated upon journal acceptance
References in corpus (100)
- Anyons in an exactly solved model and beyond
- Generalized Global Symmetries
- Topological orders and Edge excitations in FQH states
- Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
- Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
- Topological insulators in twisted transition metal dichalcogenide homobilayers
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Observation of Fractionally Quantized Anomalous Hall Effect
- Lieb-Schultz-Mattis in Higher Dimensions
- Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Coupling a QFT to a TQFT and Duality
- Reading between the lines of four-dimensional gauge theories
- Direct observation of anyonic braiding statistics at the =1/3 fractional quantum Hall state
- Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
- Fractional statistics in anyon collisions
- Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
- Nearly Flat Chern Bands in Moiré Superlattices
- Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
- Observation of half-integer thermal Hall conductance
- Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
- Condensate induced transitions between topologically ordered phases
- Towards identification of a non-abelian state: observation of a quarter of electron charge at quantum Hall state
- Fractional topological insulators
- Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
- Observation of fractional Chern insulators in a van der Waals heterostructure
- Interacting fermionic topological insulators/superconductors in three dimensions
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- On 2-Group Global Symmetries and Their Anomalies
- Comments on Chern-Simons Contact Terms in Three Dimensions
- Integer quantum Hall effect for bosons: A physical realization
- Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
- Observed Quantization of Anyonic Heat Flow
- Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
- D-brane Charges in Five-brane backgrounds
- Quantum Hall fractions in rotating Bose-Einstein condensates
- Nonconventional odd denominator fractional quantum Hall states in the second Landau level
- Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
- Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
- Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
- A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
- Spin TQFTs and fermionic phases of matter
- Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
- A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
- State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
- Fermionic Modular Categories and the 16-fold Way
- Diagrammatics for Bose condensation in anyon theories
- Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors
- Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
- Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
- Fractionalization, topological order, and quasiparticle statistics
- Boson Condensation in Topologically Ordered Quantum Liquids
- Fractional charge and fractional statistics in the quantum Hall effects
- Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
- Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
- Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
- Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
- Quantum Hall fractions for spinless Bosons
- Composite fermi liquids in the lowest Landau level
- Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected Phases
- Constraints on topological order in Mott Insulators
- In and around Abelian anyon models
- Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
- Anomalies and Symmetry Fractionalization
- Direct Observation of a Fractional Charge
- Rank-finiteness for modular categories
- The Fractional Quantum Hall States at and and their Non-Abelian Nature
- Composite fermion duality for half-filled multicomponent Landau Levels
- Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
- Collective states of non-abelian quasiparticles in a magnetic field
- Extraction of many-body Chern number from a single wave function
- Minimal nondegenerate extensions
- Fermionic symmetry fractionalization in (2+1)D
- Fractional Quantum Hall Effect at
- The enigmatic 12/5 fractional quantum Hall effect
- Lorentz Symmetry Fractionalization and Dualities in (2+1)d
- A non-Abelian parton state for the fractional quantum Hall effect
- superconductivity of composite bosons and the fractional quantum Hall effect
- Tripartite Composite Fermion States
- Fractonic order in infinite-component Chern-Simons gauge theories
- Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
- Partition Functions of Non-Abelian Quantum Hall States
- STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS
- Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
- Anomaly cascade in (2+1)D fermionic topological phases
- Anomaly indicators for topological orders with and time-reversal symmetry
- Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
- Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
- Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
- Identifying the topological order of quantized half-filled Landau levels through their daughter states
- Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
- Symmetry Transmutation and Anomaly Matching
- Gauging U(1) symmetry in (2+1)d topological phases
- Anomalous Continuous Translations
- Fractionalization as an alternate to charge ordering in electronic insulators
- (3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases
- Non-Abelian fractional quantum Hall states at filling factor 3/4
- A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders