2006/07/31 by Masaki Oshikawa, Yong Baek Kim, Kirill Shtengel +2 · 1 citation
Materials Science · Physics and Astronomy · #Charge (physics) #Degeneracy (biology) #Degenerate energy levels #Instanton #Pfaffian #Quantum many-body systems #Quasicrystal Structures and Properties #Quasiparticle #Topological Materials and Phenomena #Topological degeneracy #Topological quantum number #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1016/j.aop.2006.08.001
published as Annals of Physics 322, 1477-1498 (2007). · 28 pages, 6 figures (version 2: reference on cold atoms added + minor corrections)
arxiv created 2006/09/27 · openalex publication_date 2006/10/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.