Quantum Hall Effect in Higher Dimensions

Abstract

Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces $\mathbf{C}{P}^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\mathbf{C}{P}^2$ in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\mathbf{C}{P}^3$ is related to the case of $S^4$.

15 pages, LaTeX

Cited by in corpus (147)

• Klein-Gordon Oscillator in Kaluza-Klein Theory
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• The effective action for edge states in higher dimensional quantum Hall systems
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Bergman Kernel from Path Integral
• Goedel-type Universes and the Landau Problem
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model
• (Super)Oscillator on CP(N) and Constant Magnetic Field
• The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
• FQHE on curved backgrounds, free fields and large N
• Effective Actions of Matrix Models on Homogeneous Spaces
• Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
• 6D Fractional Quantum Hall Effect
• Quantum Hall effect on $S^3$, edge states and fuzzy $S^3/{\mathbf{Z}}_2$
• Non-commutative geometry of 4-dimensional quantum Hall droplet
• Monopole Bundles over Fuzzy Complex Projective Spaces
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Fuzzy Supersphere and Supermonopole
• Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres
• 2D and 3D topological insulators with isotropic and parity-breaking Landau levels
• Fermions in Gödel-type background space-times with torsion and the Landau quantization
• Chiral actions from phase space (quantum Hall) droplets
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• Topological insulators with SU(2) Landau levels
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Integral Coalescence Conditions In $D\ge 2$ Dimension Space
• Quantum Hall Effect on Higher Dimensional Spaces
• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Geometric construction of the Quantum Hall Effect in all even dimensions
• Quantum Hall Liquid on a Noncommutative Superplane
• Random normal matrices, Bergman kernel and projective embeddings
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Extended Supersymmetries and the Dirac Operator
• Kac-Moody theories for colored phase space (quantum Hall) droplets
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Four-dimensional Hall mechanics as a particle on $\DC P^3$
• Realization of an atomic quantum Hall system in four dimensions
• Split-Quaternionic Hopf Map, Quantum Hall Effect, and Twistor Theory
• Quantum Mechanics Model on Kähler conifold
• Isotropic Landau levels of Dirac fermions in high dimensions
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• The Geometry of Quantum Hall Effect: An Effective Action for all Dimensions
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Relativistic Landau Models and Generation of Fuzzy Spheres
• Weyl fermions in a family of Gödel-type geometries with a topological defect
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Scattering theory without large-distance asymptotics in arbitrary dimensions
• Hyperbolic Supersymmetric Quantum Hall Effect
• Higher (Odd) Dimensional Quantum Hall Effect and Extended Dimensional Hierarchy
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Monopoles and Wilson Lines
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Dyonic Instantons in 5-dim Yang-Mills Chern-Simons Theories
• Nonabelian gauge field and dual description of fuzzy sphere
• Anomalous Quantum Hall Effect on Sphere
• D-string fluid in conifold: I. Topological gauge model
• Oscillator potential for the four-dimensional Hall effect
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball
• The Quantum Hall Effect on R^4
• D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
• Instantons, Twistors, and Emergent Gravity
• Graded Hopf Maps and Fuzzy Superspheres
• Elements of (super-)Hamiltonian Formalism
• N=4 Supersymmetry and the BPST Instanton
• Hyperboloid, instanton, oscillator
• Quantum Hall Effect on the Flag Manifold F_2
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• $SO(4)$ Landau Models and Matrix Geometry
• Myers Effect and Tachyon Condensation
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Correlators of Matrix Models on Homogeneous Spaces
• Supersymmetric Chern-Simons Theory and Supersymmetric Quantum Hall Liquid
• Second moment fuzzy-field-theory-like matrix models
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$
• N=4 Supersymmetric Landau Models
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Bosonization in higher dimensions via noncommutative field theory
• Magnetic Field and Curvature Effects on Pair Production II: Vectors and Implications for Chromodynamics
• NC Effective Gauge Model for Multilayer FQH States
• Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics
• Representations and Properties of Generalized $A_r$ Statistics, Coherent States and Robertson Uncertainty Relations
• Quantum Hall Effect on Odd Spheres
• Spin-Hall effect with quantum group symmetry
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• The role of the spin connection in quantum Hall effect: A perspective from geometric quantization
• Ground state wave functions for the quantum Hall effect on a sphere and the Atiyah-Singer index theorem
• Counting Strings, Wound and Bound
• Isospin particle systems on quaternionic projective spaces
• Magnetic Field and Curvature Effects on Pair Production I: Scalars and Spinors
• ADHM and the 4d Quantum Hall Effect
• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Noncommutative Fluids
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Quantum Hall Effect on the Grassmannians ${\mathbf{Gr}}_2({\mathbb{C}}^N)$
• Phase space quantization, noncommutativity and the gravitational field
• The fermion density operator in the droplet bosonization picture
• N=8 superconformal mechanics: direct construction
• CP(n) supersymmetric mechanics in U(n) background gauge fields
• Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect
• Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them
• Second Euler number in four dimensional synthetic matter
• Geometry and large N limits in Laughlin states
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Interlayer coherence and entanglement in bilayer quantum Hall states at filling factor $\nu =2/\lambda$
• Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• New family of models for incompressible quantum liquids in $d\ge 2$
• On the Gauge-invariant Functional Measure for Gauge Fields on CP^2
• Symmetries of N=4 supersymmetric CP(n) mechanics
• A projective Dirac operator on CP^2 within fuzzy geometry
• Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem
• SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis II. The measure for gauge fields and a 4d WZW theory
• Quantum Error Correction in the Lowest Landau Level
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• The Laplacian on homogeneous spaces
• Extended Dynamical Symmetries of Landau Levels in Higher Dimensions
• SU(2) reductions in N=4 multidimensional supersymmetric mechanics
• Super Landau Models on Odd Cosets
• Matrix oscillator and Laughlin Hall states
• Fractional Quantum Hall States on CP2 Space
• Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Quantum matrix geometry in the lowest Landau level and higher Landau levels
• Fuzzy field theories and related matrix models
• Representations and Properties of Generalized $A_r$ Statistics
• Superintegrable deformations of oscillator and Coulomb systems
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature
• Non-Commutative Geometry in Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Deformation of Matrix Geometry via Landau Level Evolution
• Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution
• Electromagnetic Excitations of A_n Quantum Hall Droplets