HALL CONDUCTANCE AND EDGE STATES IN THE COULOMB GAS VERTEX OPERATOR FORMALISM

1991 ◽  
Vol 06 (32) ◽  
pp. 2985-2993 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI
Keyword(s):  
Quantum Hall ◽  
Coulomb Gas ◽  
Vertex Operators ◽  
Topological Order ◽  
Edge States ◽  
Operator Formalism ◽  
Fractional Quantum ◽  
Hall Conductance ◽  
Fractional Quantum Hall ◽  
Conformal Field

The fractional quantum Hall effect is discussed in terms of a c = 1 conformal field theory and the associated U(1) Kac–Moody current algebra, using the Coulomb gas vertex operators. A geometrical derivation of the Hall conductance is given and the possible topological order is considered. The consistency requires that only at filling ν = 1/m one of the "particles" described by the vertices can be associated with the electron.

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 MULTIPLE EDGE PARTITION FUNCTIONS FOR FRACTIONAL QUANTUM HALL STATES

1999 ◽  
Vol 14 (23) ◽  
pp. 3745-3759
Author(s):  
KAZUSUMI INO
Keyword(s):  
Quantum Hall ◽  
Multiple Edge ◽  
Partition Functions ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Verlinde Formula ◽  
Quantum Hall States ◽  
Edge Partition

We consider the multiple edge states of the Laughlin state and the Pfaffian state. These edge states are globally constrained through the operator algebra of conformal field theory in the bulk. We analyze these constraints by introducing an expression of quantum Hall state by chiral vertex operators and obtain the multiple edge partition functions by using the Verlinde formula.

THEORETICAL ASPECTS OF QUANTUM HALL EFFECT AND TWO-DIMENSIONAL CFT

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2217-2239 ◽  
Author(s):  
G. CRISTOFANO ◽  
G. MAIELLA ◽  
R. MUSTO ◽  
F. NICODEMI
Keyword(s):  
Quantum Hall ◽  
Coulomb Gas ◽  
Topological Order ◽  
Two Dimensional ◽  
Edge States ◽  
Conformal Field ◽  
Highest Weight ◽  
Finite Set ◽  
Magnetic Translation

A review of the QHE is presented where the emphasis is placed on the role of the magnetic translation group and of the related topological properties. After a presentation of general experimental and theoretical features we briefly summarize known results of two-dimensional Conformal Field Theory relevant for the QHE. Then we show how to evaluate groundstate wave functions on the plane and on the torus by the use of CFT techniques. In the latter case it is shown how for filling ν=1/m a consistent description is achieved by means of a finite set of Coulomb Gas Vertex Operators. They describe (fractional) charged particles with the associated quantized magnetic flux (“anyons"). Furthermore, from these vertices and relative highest weight states, one does find that the g.s.w.f. for the torus should be m-fold degenerate showing, also, the role of a new kind of long-range topological order recently advocated. Then we show that the presence of m sectors of edge states for a cylinder is strictly related to such a degeneracy, and their relation with a Kac-Moody algebra is discussed.

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

Topological Aspects of Quantum Hall Fluid and Berry Phase

1998 ◽  
Vol 12 (26) ◽  
pp. 2649-2707 ◽  
Author(s):  
Banasri Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Characteristic Features

We have analyzed here the recent development towards our understanding of the Integral and Fractional Quantum Hall effect. It has been pointed out that the chiral anomaly and Berry phase approach embraces in a unified way the whole spectrum of quantum Hall systems with their various characteristic features. This formalism also helps us to understand the edge states observed in Hall fluids. It is argued that Hall fluids with even denominator filling factor leads to the non-Abelian Berry phase.

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