Chiral bosonic field theories and the quantum Hall effect

2001 ◽  
Vol 79 (9) ◽  
pp. 1121-1131 ◽  
Author(s):  
P Bracken
Keyword(s):  
Hall Effect ◽  
Gauge Transformation ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Equation Of Motion ◽  
Hall Conductivity ◽  
Field Theories ◽  
Bosonic Field ◽  
Chern Simons

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

WILSON LOOPS AND NON-ABELIAN STATISTICS IN THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (17) ◽  
pp. 2875-2891
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Conductivity Tensor ◽  
Hall Conductivity ◽  
Wilson Loops ◽  
Many Body ◽  
Quantum Numbers ◽  
The Many ◽  
Chern Simons

There is a topological connection between the boundary excitations of a quantum Hall fluid and the quantum numbers of its vortex-like bulk quasi-particles. I use this connection to examine the group properties of vortex excitations in a generalized quantum Hall fluid, and show how the vortex trajectories become Wilson lines interacting via Chern-Simons fields. As a result, I argue that non-abelian statistics, if they exist, should be independent of the detailed properties of the many-body wavefunction and will depend only on the bulk Hall conductivity tensor.

CONSTRAINTS ON NONCOMMUTATIVE HALL EFFECT REVISITED

2008 ◽  
Vol 23 (26) ◽  
pp. 4361-4370 ◽  
Author(s):  
CRESUS F. L. GODINHO
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Hall Conductivity ◽  
Second Step ◽  
Direct Relation ◽  
General Constraints ◽  
Chern Simons

We consider a semiclassical formulation of the quantum Hall effect by means of an Chern–Simons gauge theory constructed for a Schrödinger field. We build up constraints managing the Faddeev–Jackiw algorithm and show a direct relation of the constraints with Hall conductivity. In the second step, we consider the noncommutative extension to the action computing the new and more general constraints and, as a right consequence, an interesting correction for the conductivity expression is found. Finally, we speculate possible interpretations of this new result and its consequences.

scholarly journals Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. U. Malakeeva ◽  
V. E. Arkhincheev
Keyword(s):  
Finite Number ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hall Current ◽  
Quantum Hall ◽  
Singular Points ◽  
Hall Conductivity

The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints).

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.

THE CHERN–SIMONS–LANDAU–GINZBURG THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (01) ◽  
pp. 25-58 ◽  
Author(s):  
SHOU CHENG ZHANG
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Physical Consequences ◽  
Systematic Derivation ◽  
Chern Simons

This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern–Simons–Landau–Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.

NON-RENORMALIZATION THEOREM IN CHERN-SIMONS THEORIES AND FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 07 (07) ◽  
pp. 611-617 ◽  
Author(s):  
A.A. OVCHINNIKOV
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Statistical Parameter ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Exact Cancellation

We prove the non-renormalization theorem resulting in the exact cancellation of Chern-Simons term (and superconductivity) in systems of both free and interacting anyons with the statistical parameter 1/N. The theorem is used to prove the quantization of transverse conductance in the proposed second-quantized fermionic description of fractional quantum Hall effect.

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