scholarly journals W-infinity symmetry in the quantum hall effect beyond the edge

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Andrea Cappelli ◽  
Lorenzo Maffi
Keyword(s):  
Field Theory ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Incompressible Fluids ◽  
Density Fluctuations ◽  
Finite Limit ◽  
Theory Approach ◽  
Conformal Field ◽  
Edge Reconstruction ◽  
Laughlin States

Abstract The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

scholarly journals TOWARD A CONFORMAL FIELD THEORY FOR THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (19) ◽  
pp. 3235-3247
Author(s):  
GREG NAGAO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Order Parameter ◽  
Quantum Hall ◽  
Cyclotron Motion ◽  
Conformal Field ◽  
Large N ◽  
Collective Coordinate

An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a "current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large N limit. An order parameter is constructed from which the Hamiltonian may be derived. This order parameter may be viewed as either a collective coordinate for a system of N charged particles in a strong magnetic field; or as a field of spins associated with the cyclotron motion of these particles.

CONNECTIONS BETWEEN THE QUANTUM HALL EFFECT AND CONFORMAL FIELD THEORY

1992 ◽  
Vol 07 (30) ◽  
pp. 2837-2849
Author(s):  
GREG NAGAO ◽  
QIAN NIU ◽  
JOSÉ GAITE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Effective Field ◽  
Vertex Operators ◽  
Effective Hamiltonian ◽  
Cyclotron Motion ◽  
Conformal Field

The quantum Hall effect (QHE) is studied in the context of a conformal field theory (CFT). Winding state vertex operators for an effective field of N "spins" associated with the cyclotron motion of particles are defined. The effective field of spins may be used to define an effective Hamiltonian. This effective Hamiltonian describes the collective motion of the N particles (with coupling κ0) together with a current-current interaction (of strength κ1). Such a system gives rise to a CFT in the large-N limit when κ0=κ1. The Laughlin wave function is derived from this CFT as an N'-point correlation function of winding state vertex operators.

scholarly journals A CONFORMAL FIELD THEORY DESCRIPTION OF THE PAIRED AND PARAFERMIONIC STATES IN THE QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (27) ◽  
pp. 1679-1688 ◽  
Author(s):  
GERARDO CRISTOFANO ◽  
GIUSEPPE MAIELLA ◽  
VINCENZO MAROTTA
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Conformal Field Theory ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Scalar Fields ◽  
Neutral Component ◽  
Conformal Field ◽  
Twisted Boundary Conditions

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in Ref. 1 to the description of a quantum Hall fluid at nonstandard fillings [Formula: see text]. The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.

THE QUANTUM HALL EFFECT AT ARBITRARY RATIONAL FILLING: A PROPOSAL

1992 ◽  
Vol 07 (28) ◽  
pp. 2583-2591 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hierarchical Model ◽  
Quantum Hall ◽  
Coulomb Gas ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Conformal Field

A description of the quantum Hall effect, already proposed for the fractional filling ν=1/m, based on the introduction of Coulomb gas-like vertex operators typical of a two-dimensional conformal field theory, is extended to the case ν=p/m. The resulting physical picture is compared with the hierarchical model.

scholarly journals FUSION AND TENSORING OF CONFORMAL FIELD THEORY AND COMPOSITE FERMION PICTURE OF FRACTIONAL QUANTUM HALL EFFECT

1996 ◽  
Vol 11 (01) ◽  
pp. 55-68 ◽  
Author(s):  
MICHAEL A.I. FLOHR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Tensor Products ◽  
Composite Fermions ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Lowest Landau Level

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of nonunitary theories, we explicitly recover Jain’s picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations — the fusion map and the tensor map — can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.

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