Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
Author:   Martin Greiter
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2011 ed.
Volume:   244
ISBN:  

9783642437823


Pages:   194
Publication Date:   01 March 2014
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains


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Overview

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.

Full Product Details

Author:   Martin Greiter
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2011 ed.
Volume:   244
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642437823


ISBN 10:   3642437826
Pages:   194
Publication Date:   01 March 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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 S = 1 spin chain.- Generalization to arbitrary spin S.- Conclusions and unresolved issues.- Spherical coordinates.- Fourier sums for one-dimensional lattices.- Angular momentum algebra.- Tensor decompositions of spin operators.

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Author Information

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

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