scholarly journals Constraint for the lowest Landau level and the Chern-Simons field-theory approach for the fractional quantum Hall effect: Infinite and finite systems

1993 ◽  
Vol 48 (4) ◽  
pp. 2347-2364 ◽  
Author(s):  
Zhong-Shui Ma ◽  
Zhao-Bin Su
Keyword(s):  
Field Theory ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Theory Approach ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Finite Systems ◽  
Lowest Landau Level ◽  
Chern Simons

COLLECTIVE FIELD THEORY APPLIED TO THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (01n02) ◽  
pp. 417-426
Author(s):  
B. Sakita ◽  
Dong-Ning Sheng ◽  
Zhao-Bin Su
Keyword(s):  
Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Dynamical Theory ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Free Vortex ◽  
Fractional Quantum Hall

We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.

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.

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