Quantum Hall Systems: Braid groups, composite fermions, and fractional charge

Abstract

The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The main formalism used in many-body quantum Hall theories -- the Chern-Simons theory is also presented. The Chern-Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall theories, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy)1). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. The introduction into multi-component quantum Hall systems and spin quantum Hall systems is sketched. 1)First condensed states of composite fermion excitations have been very recently confirmed in the experiment (Pan et al. Phys. Rev. Lett. 90 (2003) 016801). a sample of this book is available at http://www.oup.co.uk/isbn/0-19-852870-1

Table of contents, a sample of this book is available at http://www.oup.co.uk/isbn/0-19-852870-1

Cited by in corpus (10)

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• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• Coherent states on the Grassmannian $U(4)/U(2{)}^2$: Oscillator realization and bilayer fractional quantum Hall systems
• Anyons in Geometric Models of Matter
• Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations
• Lieb-Schultz-Mattis Theorem and the Filling Constraint
• Confinement and fractional charge of quarks from braid group approach to holographic principle
• Charge and Statistics of Quasiholes in Pfaffian States of Composite Fermion Excitations
• On auxiliary flux tubes associated to composite fermions in 2D Hall systems