More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation

A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, gives the “superconducting” chain that is the same as...

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Bibliographic Details
Published in:Scientific reports 2015-01, Vol.5 (1), p.8102-8102, Article 8102
Main Authors: Yu, Li-Wei, Ge, Mo-Lin
Format: Article
Language:English
Subjects:
639/766/483/481
639/766/483/640
Algebra
Commuting
Humanities and Social Sciences
multidisciplinary
Phase transitions
Physics
Science
Theoretical physics
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Summary:A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, gives the “superconducting” chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body -matrix, we thus show that the essence of the doubling degeneracy is due to . We also show that the extended Γ′-operator is an invariant of braid group B N for odd N . Moreover, with the extended Γ′-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2 N -qubit Greenberger-Horne-Zeilinger state for odd N .
ISSN:2045-2322
2045-2322
DOI:10.1038/srep08102