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.

COLLECTIVE PHENOMENA IN THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2253-2273
Author(s):  
R. FERRARI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Collective Phenomena ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Magnetic Translation

The main phenomenological features of Integer Quantum Hall Effect (IQHE) and Fractional Quantum Hall Effect (FQHE) are reviewed. A theory is proposed based on a new basis for the single particle states, given by a representation of the Magnetic Translation Group (MTG).

scholarly journals VERTEX OPERATORS AND QUANTUM HALL EFFECT

1991 ◽  
Vol 06 (04) ◽  
pp. 347-358 ◽  
Author(s):  
SERGIO FUBINI
Keyword(s):  
General Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Vertex Operator ◽  
Essential Role ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Vertex Operators ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

F.V. vertex operator which allows a consistent bosonization of fermions, bosons and anyons is shown. It thus plays an essential role in the general theory of Fractional Quantum Hall Effect (F.Q.H.E.).

THE COULOMB GAS FOR EXCITED STATES IN THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (19) ◽  
pp. 1307-1311
Author(s):  
M. HILKE ◽  
M. RUIZ-ALTABA
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Excited States ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Coulomb Gas ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Set Up

We follow Fubini's suggestion to use vertex operators for describing electrons and holes in the two-dimensional set-up appropriate for the description of the fractional quantum Hall effect, i.e., on the gauge-fixed magnetic plane. Laughlin's wave function is thus reproduced as the correlator of primary conformal fields, represented as exponentials of a free scalar field. We generalize an Ansatz by Halperin and present a new wave function describing the ground-state and the excited states of a system of unpolarized electrons. We realize these wave functions as correlators of normal-ordered exponentials of two free fields. We also give an explicit representation for the creation operator of an excitation.

scholarly journals VERTEX OPERATORS IN THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 06 (06) ◽  
pp. 487-500 ◽  
Author(s):  
S. FUBINI ◽  
C.A. LÜTKEN
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Open String ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Vertex Operators ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Holomorphic Representation

A second quantized formalism for electrons confined to a plane in a strong perpendicular magnetic field is constructed using vertex operators. They are seen to arise naturally from a holomorphic representation of Laughlin’s first quantized wave functions, since they have the unique properties of creating coherent states, satisfying anyonic statistics and factorizing matrix elements. While open string vertex operators are sufficient for representing Laughlin’s “ground state” wave functions, it is shown that the vertex operators appearing in the theory of closed strings are needed in order to represent both types of anyonic excitations (quasi-holes and quasi-electrons) which appear in the theory of the fractional quantum Hall effect.

Second Activation Energy in the Fractional Quantum Hall Effect

1987 ◽  
Vol 56 (9) ◽  
pp. 3005-3008 ◽  
Author(s):  
Junichi Wakabayashi ◽  
Satoru Sudou ◽  
Shinji Kawaji ◽  
Kazuhiko Hirakawa ◽  
Hiroyuki Sakaki
Keyword(s):  
Activation Energy ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall
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