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.

scholarly journals A TWISTED CONFORMAL FIELD THEORY DESCRIPTION OF THE QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (08) ◽  
pp. 547-555 ◽  
Author(s):  
GERARDO CRISTOFANO ◽  
GIUSEPPE MAIELLA ◽  
VINCENZO MAROTTA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ground State ◽  
Quantum Hall ◽  
Scalar Fields ◽  
Wave Functions ◽  
Charged Scalar ◽  
Conformal Field ◽  
Charged Scalar Field ◽  
Twisted Boundary Conditions

We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows one to describe a quantum Hall fluid at Jain hierarchical filling, [Formula: see text], in terms of one charged scalar field and m - 1 neutral ones. Then the resulting algebra of the chiral primary fields is U(1)×[Formula: see text]. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons).

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.

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.

scholarly journals A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Ajit Coimbatore Balram
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Topological Structure ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

scholarly journals BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4497-4591 ◽  
Author(s):  
MICHAEL A. I. FLOHR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Hall ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Verlinde Formula

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

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