Mapping of Parent Hamiltonians

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction and Summary

   • Martin Greiter

   Pages 1-10

3. Three Models and a Ground State

   • Martin Greiter

   Pages 11-77

4. From a Laughlin State to the Haldane–Shastry Model

   • Martin Greiter

   Pages 79-107

5. From a Bosonic Pfaffian State to an \(\boldsymbol{\it S}\,{=}\,1\) Spin Chain

   • Martin Greiter

   Pages 109-140

6. Generalization to Arbitrary Spin \(\boldsymbol{\it{S}}\)

   • Martin Greiter

   Pages 141-172

7. Conclusions and Unresolved Issues

   • Martin Greiter

   Pages 173-178

8. Back Matter

   Pages 179-194

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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

• Institut f. Theorie der, Kondensierten Materie, KIT, Karlsruhe, Germany

  Martin Greiter

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

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