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Theory of Quantum Hall States

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.07
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Quantization of Many-Particle Systems and Quantum Statistics in Lower Dimensions

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs

in Quantum Hall systems: Braid groups, composite fermions and fractional charge

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198528708
eISBN:
9780191713477
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528708.003.0003
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter describes how, in two-dimensional systems, the scalar fractional statistics may occur besides Bose–Einstein and Fermi–Dirac statistics. One-dimensional irreducible unitary ... More


Introduction

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs

in Quantum Hall systems: Braid groups, composite fermions and fractional charge

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198528708
eISBN:
9780191713477
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528708.003.0001
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This introductory chapter starts with short review of experimental and theoretical description of integral and fractional quantum Hall effects. The standard quantization of states of charged ... More


Topological and Quantum order—beyond Landau’s Theories

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.08
Subject:
Physics, Theoretical, Computational, and Statistical Physics

According to the principle of emergence, the properties of material are mainly determined by how the atoms are organized in the material. Such organization is formally called order. The vast range of ... More


Topological field theory

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0031
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Topological field theories are discussed and this chapter provides some concrete examples of applications of these ideas by discussing anyons, fractional statistics and Chern–Simons theories.


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