Mapping of Parent Hamiltonians
From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
Nonfiction, Science & Nature, Science, Physics, Solid State Physics, Quantum Theory
| Author: | Martin Greiter | ISBN: | 9783642243844 |
| Publisher: | Springer Berlin Heidelberg | Publication: | December 4, 2011 |
| Imprint: | Springer | Language: | English |
| Author: | Martin Greiter |
| ISBN: | 9783642243844 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | December 4, 2011 |
| Imprint: | Springer |
| Language: | English |
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.
