Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect

Abstract

A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1) gauge symmetry for an emergent holomorphic symmetry and fluxes for vortices. The novel holomorphic invariance is used to develop an analytical method for attaching vortices to particles. Vortex attachment methods introduced in this paper are subsequently employed to construct the Read operator within a second quantized framework and obtain the Laughlin and Jain wave functions as exact results entirely within a mean-field approximation. The gauge invariant framework and vortex attachment techniques are generalized to the case of spherical geometry and spherical counterparts of Laughlin and Jain wave functions are also obtained exactly within MFT.

arXiv comment33 pages, no figures. Several Typos corrected in latest version

References in corpus (29)

• Is the Composite Fermion a Dirac Particle?
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Quantum Hall Effect in Higher Dimensions
• Dual Dirac liquid on the surface of the electron topological insulator
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Towards a field theory of the fractional quantum Hall states
• Response functions and Spectrum of Collective Excitations of Fractional Quantum Hall Effect Systems
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• A Self-consistent Inclusion of Magnetic Screening for the Quark-Gluon Plasma
• Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• The effective action for edge states in higher dimensional quantum Hall systems
• On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions
• Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model
• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• A Field Theory for the Read Operator
• Gauge-invariant Variables and Entanglement Entropy
• Algebraic Aspects of the Fractional Quantum Hall Effect
• Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects
• $W_{\infty }$ Algebras in the Quantum Hall Effect
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• Anyons on the sphere: analytic states and spectrum
• The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$
• Ground state wave functions for the quantum Hall effect on a sphere and the Atiyah-Singer index theorem
• The Conformal Spectrum of Non-Abelian Anyons
• Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$
• Fermions, Mass-Gap and Landau Levels: Gauge invariant Hamiltonian for QCD in D=2+1