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Majorana fermions in the nonuniform Ising-Kitaev chain : exact solution

Narozhny, Boris

Abstract:
A quantum computer based on Majorana qubits would contain a large number of zero-energy Majorana states. This system can be modelled as a connected network of the Ising-Kitaev chains alternating the “trivial” and “topological” regions, with the zero-energy Majorana fermions localized at their interfaces. The low-energy sector of the theory describing such a network can be formulated in terms of leading-order couplings between the Majorana zero modes. I consider a minimal model exhibiting effective couplings between four Majorana zero modes – the nonuniform Ising-Kitaev chain, containing two “topological” regions separated by a “trivial” region. Solving the model exactly, I show that for generic values of the model parameters the four zero modes are localized at the four interface points of the chain. In the special case where additional inversion symmetry is present, the Majorana zero modes are “delocalized” between two interface points. In both cases, the low-energy sector of the theory can be formulated in terms of the localized Majorana fermions, but the couplings between some of them are independent of their respective separatio ... mehr


Zugehörige Institution(en) am KIT Institut für Theorie der Kondensierten Materie (TKM)
Publikationstyp Zeitschriftenaufsatz
Jahr 2017
Sprache Englisch
Identifikator DOI: 10.1038/s41598-017-01413-z
ISSN: 2045-2322
URN: urn:nbn:de:swb:90-701421
KITopen ID: 1000070142
Erschienen in Scientific reports
Band 7
Heft 1
Seiten Art.Nr. 1447
Lizenz CC BY 4.0: Creative Commons Namensnennung 4.0 International
Bemerkung zur Veröffentlichung Gefördert durch den KIT-Publikationsfonds
Schlagworte Quantum information; Statistical physics; Theoretical physics
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