Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

by Martin Greiter

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.

Product Details

ISBN-13:	9783642243844
Publisher:	Springer-Verlag New York, LLC
Publication date:	12/04/2011
Series:	Springer Tracts in Modern Physics , #244
Sold by:	Barnes & Noble
Format:	eBook
File size:	16 MB
Note:	This product may take a few minutes to download.

About the Author

PHD Martin Greiter
Karlsruhe Institute of Technology, KIT, Germany
[e-mail]

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.