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Quantum Field Theory of Many-Body SystemsFrom the Origin of Sound to an Origin of Light and Electrons$
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Xiao-Gang Wen

Print publication date: 2007

Print ISBN-13: 9780199227259

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199227259.001.0001

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Theory of Quantum Hall States

Theory of Quantum Hall States

Quantum Field Theory of Many-Body Systems

Xiao-Gang Wen

Oxford University Press

Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. FQH states cannot be described by Landau symmetry breaking theory. These shatter the long-held belief that symmetry breaking theory describes all phases and phase transitions. As a result, a completely new theory is needed to describe FQH states, and this is the topic of this chapter. Many-electron systems in strong magnetic fields and resulting Landau level structures are studied. Laughlin's theory and the hierarchical theory for FQH effect are presented. The chapter then derives the low energy effective Chern–Simons theory for FQH states and discusses the resulting fractional charge and fractional statistics, as well as the K-matrix classification of Abelian FQH states. The theory of chiral gapless edge states is also introduced, where experimental predictions can be made.

Keywords:   FQH effect, Laughlin state, hierarchical state, fractional charge, fractional statistics, Chern-Simons theory, edge state, conformal field theory, bosonization

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