scholarly journals Conformal field theory approach to bulk wave functions in the fractional quantum Hall effect

2003 ◽  
Vol 67 (23) ◽  
Author(s):  
Michael Flohr ◽  
Klaus Osterloh
Keyword(s):  
Field Theory ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Theory Approach ◽  
Bulk Wave ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field

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.

A Microscopic Hierarchy Theory of the Fractional Quantum Hall Effect

1997 ◽  
Vol 11 (06) ◽  
pp. 707-728 ◽  
Author(s):  
Jian Yang ◽  
Wu-Pei Su
Keyword(s):  
Quantum Hall Effect ◽  
Ground State ◽  
Collective Excitation ◽  
Quantum Hall ◽  
Electron System ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Hierarchy Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

In this paper we present a microscopic hierarchy theory of the fractional quantum Hall effect. The wave functions of the ground state and the collective excitation states are obtained in terms of the electron coordinates. Working in the subspace spanned by the quasiparticles of the 1/m L Laughlin ground state, with m L an odd integer, it is shown that there exists a simple mapping between electron states in the quasiparticle subspace and states of an auxiliary boson system which is defined such that the number of the bosons is the same as that of the quasiparticles and the total magnetic flux quanta seen by the bosons equals the number of electrons. For the auxiliary boson system, one can write down the Laughlin state as well as the density wave states, analogous to the electron system at filling factor 1/m L . By mapping these states onto the quasiparticle subspace of the electrons, we find that the resulting wave functions provide a quite good description for the ground state and the collective excitations respectively of the original electron system at filling factor ν=1/(m L (± 1/2p)) with p a positive integer. This construction of the ground state and the collective excitation states can be repeated for higher filling factors. The theory presented in this paper can be viewed as a microscopic realization of Haldane's original hierarchy picture.

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