scholarly journals Construction of a series of new ν=2/5 fractional quantum Hall wave functions by conformal field theory

2020 ◽  
Vol 102 (11) ◽  
Author(s):  
Li Chen ◽  
Kun Yang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Hall ◽  
Wave Functions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field

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.

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 On the Constraint Equation for the Lowest Landau Level in Fractional Quantum Hall System

1991 ◽  
Vol 05 (10) ◽  
pp. 1715-1724 ◽  
Author(s):  
Dong-Ning Sheng ◽  
Zhao-Bin Su ◽  
B. Sakita
Keyword(s):  
Field Theory ◽  
Landau Level ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Wave Functions ◽  
Generic Properties ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Quantum Hall System

In the framework of collective field theory, We apply the Chern-Simon field theory treatment to the constraint equation for the lowest Landau level to investigate the generic properties for the quasi-particles of the FQH system. It shows a transparent connection to the Laughlin's wave functions. If we take an average over the wave functional for the constraint equation, the resulted equation can be interpreted as the vortex equation for the fractionally charged quasi-particles. Introducing a generalized ρ (density)-ϑ (phase) transformation, not only the fractional statistics and the hierarchy scheme can be drawn from the constraint equation, it also gives rise an interesting picture that vortices condense as a Halperin like wave fuction on a Laughlin like background condensate of ν=1/m.

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 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.

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