© 2011

Mapping of Parent Hamiltonians

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

  • Integrates classic material and new concepts

  • Presents precise and reproducible accounts of model discovery

  • Inspires students and researchers to further advances in this field


Part of the Springer Tracts in Modern Physics book series (STMP, volume 244)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Martin Greiter
    Pages 1-10
  3. Martin Greiter
    Pages 11-77
  4. Martin Greiter
    Pages 173-178
  5. Back Matter
    Pages 179-194

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.


Abelian and non-Abelian statistics Critical model Exact models Haldane-Shastry Model Integrable models Laughlin state Pfaffian state Quantum Hall states Spin chains Wess-Zumino Witten model

Authors and affiliations

  1. 1.Institut f. Theorie der, Kondensierten MaterieKITKarlsruheGermany

About the authors

PHD Martin Greiter
Karlsruhe Institute of Technology, KIT, Germany

Bibliographic information

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