Vertex operators and spinon edge excitations in the spin-singlet quantum Hall effect

1991 ◽  
Vol 43 (10) ◽  
pp. 8038-8043 ◽  
Author(s):  
Alexander Balatsky ◽  
Michael Stone
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Vertex Operators ◽  
Spin Singlet

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (03) ◽  
pp. 509-527 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Group Action ◽  
Quantum Hall ◽  
Vertex Operators ◽  
Edge States ◽  
Many Body ◽  
Level I ◽  
The Many

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-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.

A COULOMB GAS DESCRIPTION OF THE COLLECTIVE STATES FOR THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 06 (19) ◽  
pp. 1779-1786 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Coulomb Gas ◽  
Fractional Quantum Hall Effect ◽  
Irreducible Representations ◽  
Vertex Operators ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Magnetic Translation

Many anyons wavefunctions relevant for the fractional Quantum Hall Effect at filling ν = 1/m are obtained by using Coulomb gas conformal Vertex operators. They provide irreducible representations of a subgroup of the magnetic translation group on the torus and their degeneracy is related to the allowed set of anyonic charges.

scholarly journals Half-integral spin-singlet quantum Hall effect

1993 ◽  
Vol 48 (20) ◽  
pp. 15245-15249 ◽  
Author(s):  
L. Belkhir ◽  
X. G. Wu ◽  
J. K. Jain
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Spin Singlet ◽  
Integral Spin
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