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Title: Vortex loops and Majoranas

We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We give some general results and then focus on ladder Hamiltonian examples as a test of further ideas. Two methods yield exact results: (i) A mapping of certain spin Hamiltonians to quartic interactions of Majoranas shows that the spectra of these two examples coincide. (ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices in the ground states. Two additional methods suggest wider applicability of these results: (iii) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. (iv) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [4] ;  [5] ;  [4] ;  [6]
  1. Department of Physics, McGill University, Montreal, Quebec H3A 2T8 (Canada)
  2. (Japan)
  3. Harvard University, Cambridge, Massachusetts 02138 (United States)
  4. (Switzerland)
  5. CEMS, RIKEN, Wako, Saitama 351-0198 (Japan)
  6. Department of Physics, University of Basel, Basel (Switzerland)
Publication Date:
OSTI Identifier:
22251431
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENSTATES; GROUND STATES; HAMILTONIANS; INTERACTIONS; MAPPING; REFLECTION; SPECTRA; SPIN