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THE HIERARCHY THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT
- Source :
- Modern Physics Letters B. :57-70
- Publication Year :
- 1993
- Publisher :
- World Scientific Pub Co Pte Lt, 1993.
-
Abstract
- A recently developed hierarchy theory of the fractional quantum Hall effect (FQHE) is reviewed in this article. We use a many quasiparticle (QP) wave function to obtain the effective partition function of a FQHE system in the path-integral representation, which has been shown to be formally equivalent to an anyon system confined to the lowest Landau level. However the two systems are different in the dimension of the Hilbert space, which implies that the standard hierarchy theory is invalid beyond second hierarchical states. The only way to overcome the difficulty is to place anyons in higher Landau levels. By making a mean-field approximation to the statistical gauge field, the QPs are converted to bosons and a constraint boson system is derived. We find a new type of condensate of the bosonic QPs, which results in a new type of incompressible states of the electrons. These states which involve only two hierarchies should have higher stability over others. That explains why some sequences of filling fractions occur prominently in experiment. Finally, we show that there is a one-to-one correspondence between the new hierarchy theory and the composite fermion theory proposed by Jain.
- Subjects :
- Physics
Anyon
Statistical and Nonlinear Physics
Landau quantization
Partition function (mathematics)
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
Condensed Matter Physics
Topological quantum computer
Theoretical physics
Quantum mechanics
Fractional quantum Hall effect
Composite fermion
Quasiparticle
Gauge theory
Subjects
Details
- ISSN :
- 17936640 and 02179849
- Database :
- OpenAIRE
- Journal :
- Modern Physics Letters B
- Accession number :
- edsair.doi...........341b4a91152f88da328cb505aaf8d7e1