Mapping of Parent Hamiltonians
From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
Seiten
2014
|
2011
Springer Berlin (Verlag)
978-3-642-43782-3 (ISBN)
Springer Berlin (Verlag)
978-3-642-43782-3 (ISBN)
Unlike the spinons in the Haldane-Shastry model, those proposed here obey non-abelian statistics and integrate classical and fresh concepts. The new model this volume introduces is derived by mapping exact models of quantized Hall states into spin chains.
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.
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.
PHD Martin Greiter Karlsruhe Institute of Technology, KIT, Germany greiter@tkm.uni-karlsruhe.de
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.
| Erscheint lt. Verlag | 1.3.2014 |
|---|---|
| Reihe/Serie | Springer Tracts in Modern Physics |
| Zusatzinfo | XIV, 194 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 326 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | 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 |
| ISBN-10 | 3-642-43782-6 / 3642437826 |
| ISBN-13 | 978-3-642-43782-3 / 9783642437823 |
| Zustand | Neuware |
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