Overview

Authors:

Martin Greiter ⁰

Martin Greiter
1. Institut f. Theorie der, Kondensierten Materie, KIT, Karlsruhe, Germany
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Integrates classic material and new concepts
Presents precise and reproducible accounts of model discovery
Inspires students and researchers to further advances in this field
Includes supplementary material: sn.pub/extras

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

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Table of contents (6 chapters)

Front Matter

Pages i-xiv

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Introduction and Summary
- Martin Greiter
Pages 1-10
Three Models and a Ground State
- Martin Greiter
Pages 11-77
From a Laughlin State to the Haldane–Shastry Model
- Martin Greiter
Pages 79-107
From a Bosonic Pfaffian State to an \(\boldsymbol{\it S}\,{=}\,1\) Spin Chain
- Martin Greiter
Pages 109-140
Generalization to Arbitrary Spin \(\boldsymbol{\it{S}}\)
- Martin Greiter
Pages 141-172
Conclusions and Unresolved Issues
- Martin Greiter
Pages 173-178
Back Matter

Pages 179-194

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Keywords

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.

Authors and Affiliations

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

Martin Greiter

About the author

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

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: Martin Greiter
Series Title: Springer Tracts in Modern Physics
DOI: https://doi.org/10.1007/978-3-642-24384-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-24383-7Published: 07 December 2011
Softcover ISBN: 978-3-642-43782-3Published: 01 March 2014
eBook ISBN: 978-3-642-24384-4Published: 04 December 2011
Series ISSN: 0081-3869
Series E-ISSN: 1615-0430
Edition Number: 1
Number of Pages: XIV, 194
Topics: Quantum Physics, Solid State Physics, Complex Systems, Mathematical Methods in Physics, Mathematical Physics, Statistical Physics and Dynamical Systems

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Mapping of Parent Hamiltonians

Overview

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Table of contents (6 chapters)

Front Matter

Introduction and Summary

Three Models and a Ground State

From a Laughlin State to the Haldane–Shastry Model

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

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

Conclusions and Unresolved Issues

Back Matter

Keywords

About this book

Authors and Affiliations

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

About the author

Bibliographic Information

Publish with us

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