Chern-Simons Ginzburg-Landau Theory of the Fractional Quantum Hall System with Edges

1994 ◽  
pp. 168-174 ◽  
Author(s):  
N. Nagaosa ◽  
M. Kohmoto
Keyword(s):  
Landau Theory ◽  
Quantum Hall ◽  
Ginzburg Landau ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall System ◽  
Chern Simons

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 CHARGED VORTEX DYNAMICS IN GINZBURG–LANDAU THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1995 ◽  
Vol 10 (05) ◽  
pp. 645-666 ◽  
Author(s):  
THEODORE J. ALLEN ◽  
ANDREW J. BORDNER
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Order Parameter ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Effective Theory ◽  
Ginzburg Landau ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Motion

We write a Ginzburg–Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2 + 1 dimensions, which we propose as an effective theory for the fractional quantum Hall effect. We further propose to identify vortex excitations of the theory with Laughlin's fractionally charged quasiparticles. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two-dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.

scholarly journals Measurement of the specific heat of a fractional quantum Hall system

2007 ◽  
Vol 76 (15) ◽  
Author(s):  
F. Schulze-Wischeler ◽  
U. Zeitler ◽  
C. v. Zobeltitz ◽  
F. Hohls ◽  
D. Reuter ◽  
...  
Keyword(s):  
Specific Heat ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall System

scholarly journals A FAMILY OF NONCOMMUTATIVE GEOMETRIES

2011 ◽  
Vol 26 (29) ◽  
pp. 2213-2221 ◽  
Author(s):  
DEBABRATA SINHA ◽  
PULAK RANJAN GIRI
Keyword(s):  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
The Self ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Adjoint Extension ◽  
Quantum Hall System ◽  
Extension Parameter

It is shown that the noncommutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of noncommutative geometry labeled by the self-adjoint extension parameters. We explicitly perform an exact calculation using a singular interaction and show that, when projected to a certain Landau level, the emergent noncommutative geometries of the projected coordinates belong to a one-parameter family. There is a possibility of obtaining the filling fraction of fractional quantum Hall effect by suitably choosing the value of the self-adjoint extension parameter.

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