 Authors
 Title
 A conformal field theory description of fractional quantum Hall states
 Supervisors
 Award date
 24 April 2002
 Number of pages
 135
 ISBN
 9057760843
9789057760846  Document type
 PhD thesis
 Faculty
 Faculty of Science (FNWI)
 Institute
 Institute for Theoretical Physics Amsterdam (ITFA)
 Abstract

In this thesis, we give a description of fractional quantum Hall states in terms of conformal field theory (CFT). As was known for a long time, the Laughlin states could be written in terms of correlators of chiral vertex operators of a c=1 CFT. It was shown by G. Moore and N. Read that more general constructions are possible, and they proposed a new quantum Hall state, which has an underlying pairing structure. Related to that, it turned out that the quasiparticle excitations obey nonabelian statistics. The machienery of conformal field theory can be used to define and study more general paired, or clustered quantum Hall states, with or without spin. In this thesis, we focused on two classed of clustered (nonabelian) quantum Hall states, namely a spin polarized series, defined by N. Read and E. Rezayi and a spinsinglet series, which we proposed. These states, with or without quasiparticles, can be defined as conformal correlators in certain CFTs with an underlying affine Lie algebra symmetry. We determined the Kmatrices, which describe the topological properties of the quantum Hall states. To find them, we used a generalization of the concept, to include composite particles, and, related to that, so called pseudoparticles, which account for the nonabelian statistics. In fact, clustering structure of the states is intimately related to the nonabelian statistics of the quasiparticles. The Kmatrices also play an important role in the characters of the conformal field theories. Using the methods alluded to above, we studied the properties of the quasiparticle excitations. Another way of studying these quasiparticle exciations is by numerically diagonalizing electrons on the sphere, in the presence of a magnetic field. The interactions between the electrons are taken in such a way that the quantum Hall state is the unique ground state for a certain amount of flux quanta. By increasing the flux, quasiparticles are induced, and the groud state becomes degenerate. This degenaracy can be understood in terms of the conformal field theory describing the quantum Hall states and we were able to give an explicit formula for this degenaracy.
 Note
 Research conducted at: Universiteit van Amsterdam
 Permalink
 http://hdl.handle.net/11245/1.199883
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Thesis

Cover

Stellingen

Titlepage

Contents

Introduction

Chapter 1 The quantum Hall effect

Chapter 2 The quantum Hall  conformal field theory connection

Chapter 3 Clustered quantum Hall states

Chapter 4 Statistics properties

Chapter 5 Kmatrices for clustered quantum Hall states

Chapter 6 State counting for clustered quantum Hall states

Epilogue

Bibliography

Samenvatting

Dankwoord

Cover

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