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.

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 HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (14) ◽  
pp. 2655-2665 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Simons Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Chern Simons Theory

One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

scholarly journals CHERN–SIMONS THEORY OF FRACTIONAL QUANTUM HALL EFFECT IN (PSEUDO) MASSLESS DIRAC ELECTRONS

2011 ◽  
Vol 25 (20) ◽  
pp. 2779-2785
Author(s):  
HUABI ZENG
Keyword(s):  
Quantum Hall ◽  
Effective Field ◽  
Simons Theory ◽  
Arbitrary Integer ◽  
Fractional Quantum ◽  
Hall Conductance ◽  
Fractional Quantum Hall ◽  
Topological Excitations ◽  
Chern Simons ◽  
Chern Simons Theory

We derive the effective-field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be σxy=e2/h(2k-1) where k is arbitrary integer. There are also topological excitations which have fractional charge and obey fractional statistics.

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