scholarly journals Gamma(2) modular symmetry, renormalization group flow and the quantum hall effect

1999 ◽  
Vol 33 (1) ◽  
pp. 39-55 ◽  
Author(s):  
Yvon Georgelin ◽  
Thierry Masson ◽  
Jean-Christophe Wallet
Keyword(s):  
Renormalization Group ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Renormalization Group Flow ◽  
Group Flow

scholarly journals $\bm{\widehat{{\rm U}(1)}\times\widehat{{\rm SU}({\lc m})}_{1}}$ THEORY AND c=m W1+∞ MINIMAL MODELS IN THE HIERARCHICAL QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (06) ◽  
pp. 915-926 ◽  
Author(s):  
MARINA HUERTA
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Quantum Hall ◽  
Detailed Comparison ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
Group Flow

Two classes of Conformal Field Theories have been proposed to describe the Hierarchical Quantum Hall Effect: the multicomponent bosonic theory, characterized by the symmetry [Formula: see text] and the W1+∞ minimal models with central charge c=m. In spite of having the same spectrum of edge excitations, they manifest differences in the degeneracy of the states and in the quantum statistics, which call for a more detailed comparison between them. Here, we describe their detailed relation for the general case, c=m and extend the methods previously published for c≤3. Specifically, we obtain the reduction in the number of degrees of freedom from the multicomponent Abelian theory to the minimal models by decomposing the characters of the [Formula: see text] representations into those of the c=mW1+∞ minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W1+∞ minimal models as an infrared fixed point.

scholarly journals QUANTUM HALL TRANSITION IN THE CLASSICAL LIMIT

2001 ◽  
Vol 15 (09) ◽  
pp. 1225-1238 ◽  
Author(s):  
V. GURARIE ◽  
A. ZEE
Keyword(s):  
Correlation Function ◽  
Renormalization Group ◽  
Electron Density ◽  
Classical Limit ◽  
Quantum Hall ◽  
Renormalization Group Flow ◽  
Density Correlation ◽  
Normal Diffusion ◽  
Group Flow ◽  
Natural Way

We study the quantum Hall transition using the density–density correlation function. We show that in the limit ℏ → 0 the electron density moves along the percolating trajectories, undergoing normal diffusion. The localization exponent coincides with its percolation value ν=4/3. The framework provides a natural way to study the renormalization group flow from percolation to quantum Hall transition. We also confirm numerically that the critical conductivity of a classical limit of quantum Hall transition is [Formula: see text].

Localization and many-body interactions in the quantum Hall effect determined by polarized optical emission

1991 ◽  
Vol 44 (8) ◽  
pp. 4006-4009 ◽  
Author(s):  
B. B. Goldberg ◽  
D. Heiman ◽  
M. Dahl ◽  
A. Pinczuk ◽  
L. Pfeiffer ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Optical Emission ◽  
Many Body ◽  
Many Body Interactions

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System
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