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.
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November 2013
Research Article|
November 15 2013
Vortex loops and Majoranas
Stefano Chesi;
Stefano Chesi
1Department of Physics,
McGill University
, Montreal, Quebec H3A 2T8, Canada
2
CEMS
, RIKEN, Wako, Saitama 351-0198, Japan
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Arthur Jaffe;
Arthur Jaffe
3
Harvard University
, Cambridge, Massachusetts 02138, USA
4Department of Physics,
University of Basel
, Basel, Switzerland
5Institute for Theoretical Physics,
ETH Zürich
, Zürich, Switzerland
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Daniel Loss;
Daniel Loss
2
CEMS
, RIKEN, Wako, Saitama 351-0198, Japan
4Department of Physics,
University of Basel
, Basel, Switzerland
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Fabio L. Pedrocchi
Fabio L. Pedrocchi
4Department of Physics,
University of Basel
, Basel, Switzerland
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J. Math. Phys. 54, 112203 (2013)
Article history
Received:
September 24 2013
Accepted:
October 23 2013
Citation
Stefano Chesi, Arthur Jaffe, Daniel Loss, Fabio L. Pedrocchi; Vortex loops and Majoranas. J. Math. Phys. 1 November 2013; 54 (11): 112203. https://doi.org/10.1063/1.4829273
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