scholarly journals Analytic wave functions for neutral bulk excitations in fractional quantum Hall fluids

2013 ◽  
Vol 87 (24) ◽  
Author(s):  
Bo Yang
Keyword(s):  
Quantum Hall ◽  
Wave Functions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Analytic Wave

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.

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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