scholarly journals On the Constraint Equation for the Lowest Landau Level in Fractional Quantum Hall System

1991 ◽  
Vol 05 (10) ◽  
pp. 1715-1724 ◽  
Author(s):  
Dong-Ning Sheng ◽  
Zhao-Bin Su ◽  
B. Sakita
Keyword(s):  
Field Theory ◽  
Landau Level ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Wave Functions ◽  
Generic Properties ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Quantum Hall System

In the framework of collective field theory, We apply the Chern-Simon field theory treatment to the constraint equation for the lowest Landau level to investigate the generic properties for the quasi-particles of the FQH system. It shows a transparent connection to the Laughlin's wave functions. If we take an average over the wave functional for the constraint equation, the resulted equation can be interpreted as the vortex equation for the fractionally charged quasi-particles. Introducing a generalized ρ (density)-ϑ (phase) transformation, not only the fractional statistics and the hierarchy scheme can be drawn from the constraint equation, it also gives rise an interesting picture that vortices condense as a Halperin like wave fuction on a Laughlin like background condensate of ν=1/m.

W INFINITE SYMMETRIES IN THE HIERARCHICAL QUASIPARTICLE STATES (LOWEST LANDAU LEVEL STATES) OF THE FRACTIONAL QUANTUM HALL SYSTEMS

1995 ◽  
Vol 09 (02) ◽  
pp. 195-219
Author(s):  
YI-XIN CHEN ◽  
ZHONG-SHUI MA ◽  
ZHAO-BIN SU
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Symmetric Algebra ◽  
Operator Product ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Symmetric Algebras ◽  
Lowest Landau Level ◽  
Quantum Hall System ◽  
Infinite Symmetries

We investigate the W infinite symmetries in the theory of general fractional quantum Hall effects by using the lowest Landau level constraint approach. We find that there does exist a W infinite symmetric algebra for the fractional quantum Hall system with all the quasiparticles being restricted to the lowest Landau level. The corresponding generators can be used to generate the new degenerate wavefunctions of the lowest Landau level states by means of Laughlin and Halperin wavefunctions. Meanwhile, we find there still exists another W infinite symmetric algebra in the system, whose generators are used to generate the degenerate wavefunctions of the lowest Landau level for the anti-quasiparticles. We conclude that the FQH system can effectively be described by quasiparticle features or anti-quasiparticle features. We also show that the local part of the W infinite symmetric algebras is the magnetic translation operator of the general fractional quantum Hall system. We finally construct the operators of the single mode wave density excitations in the system and discuss their operator product relations.

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 Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

1997 ◽  
Vol 11 (22) ◽  
pp. 2621-2660 ◽  
Author(s):  
J. K. Jain ◽  
R. K. Kamilla
Keyword(s):  
Landau Level ◽  
Ground State ◽  
Quantum Hall ◽  
Monte Carlo Study ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Standard Manner

Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

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