Vortex loops and Majoranas
Abstract
We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We first give some general results, and then we focus on ladder Hamiltonian examples to test further ideas. Two methods yield exact results: i.) We utilize the mapping of spin Hamiltonians to quartic interactions of Majoranas and show under certain conditions the spectra of these two examples coincide. ii) In cases with reflectionsymmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices. Aside from these exact results, 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 2013
 DOI:
 10.1063/1.4829273
 arXiv:
 arXiv:1305.6270
 Bibcode:
 2013JMP....54k2203C
 Keywords:

 03.65.w;
 02.10.Ud;
 Quantum mechanics;
 Linear algebra;
 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics
 EPrint:
 28 pages