Journal
ANNALS OF PHYSICS
Volume 322, Issue 6, Pages 1477-1498Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2006.08.001
Keywords
non-Abelian statistics; topological order; topological degeneracy; fractional quantum Hall effect; Pfaffian states; Majorana fermion; p plus ip superconductor; spin structure; index theorem
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Funding
- Ministry of Education, Science & Technology (MoST), Republic of Korea [PG018402] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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., T. Senthil, Phys. Rev. Lett. 96 (2006) 060601] which relates fractionalization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61 (2000) 10267] 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. (C) 2006 Elsevier Inc. All rights reserved.
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