Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains (Springer Tracts in Modern Physics Book 244)

"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."--Publisher's website Front Matter....Pages i-xiv Introduction and Summary....Pages 1-10 Three Models and a Ground State....Pages 11-77 From a Laughlin State to the Haldane–Shastry Model....Pages 79-107 From a Bosonic Pfaffian State to an $$\boldsymbol{\it S}\,{=}\,1$$ Spin Chain....Pages 109-140 Generalization to Arbitrary Spin $\boldsymbol{\it{S}}$ ....Pages 141-172 Conclusions and Unresolved Issues....Pages 173-178 Back Matter....Pages 179-194