Springer Tracts in Modern Physics

Mapping of Parent Hamiltonians

From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

Authors: Greiter, Martin

  • Integrates classic material and new concepts
  • Presents precise and reproducible accounts of model discovery
  • Inspires students and researchers to further advances in this field
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About this book

This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2.  While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics.  This manifests itself through topological choices for the fractional momentum spacings.  The general model is derived by mapping exact models of quantized Hall states onto spin chains.  The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.

About the authors

PHD Martin Greiter
Karlsruhe Institute of Technology, KIT, Germany
greiter@tkm.uni-karlsruhe.de

Table of contents (6 chapters)

  • Introduction and Summary

    Greiter, Martin

    Pages 1-10

  • Three Models and a Ground State

    Greiter, Martin

    Pages 11-77

  • From a Laughlin State to the Haldane–Shastry Model

    Greiter, Martin

    Pages 79-107

  • From a Bosonic Pfaffian State to an $$\boldsymbol{\it S}\,{=}\,1$$ Spin Chain

    Greiter, Martin

    Pages 109-140

  • Generalization to Arbitrary Spin $\boldsymbol{\it{S}}$

    Greiter, Martin

    Pages 141-172

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-642-24384-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-642-24383-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-43782-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mapping of Parent Hamiltonians
Book Subtitle
From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
Authors
Series Title
Springer Tracts in Modern Physics
Series Volume
244
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-24384-4
DOI
10.1007/978-3-642-24384-4
Hardcover ISBN
978-3-642-24383-7
Softcover ISBN
978-3-642-43782-3
Series ISSN
0081-3869
Edition Number
1
Number of Pages
XIV, 194
Topics