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

• Main Author: Greiter, Martin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Springer Tracts in Modern Physics, 244
• Subjects: Physics.; Mathematical physics.; Quantum physics.; Solid state physics.; Statistical physics.; Dynamical systems.; Quantum Physics.; Solid State Physics.; Statistical Physics, Dynamical Systems and Complexity.; Mathematical Methods in Physics.; Mathematical Physics.

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-abe...

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.