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

TL;DR

This book explores the theoretical and numerical aspects of quantum Hall systems, focusing on braid groups, composite fermions, fractional charge, and hierarchical states, providing a comprehensive overview of the field.

Contribution

It develops the braid group formalism for anyons and composite fermions, and presents detailed Chern-Simons theory applications and numerical studies in quantum Hall systems.

Findings

Numerical confirmation of composite fermion condensed states

Hierarchy of odd- and even-denominator quantum Hall states

Discussion of BCS paired Hall state

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