Abstract
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 BN 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 2N-qubit Greenberger-Horne-Zeilinger state for odd N.
Highlights
On the other hand, based on the obtained new type of solution RiðhÞ of Yang-Baxter equation (YBE), which is related to Majorana operators, the corresponding Hamiltonian can be found by following the standard way[9], i.e
We show that the emergent Majorana operator C is a new symmetry of RðhÞ as well as Yang-Baxter equation
The topological phase transition in the derived ‘‘superconducting’’ chain based on YBE is discussed
Summary
-matrix, we show that the essence of the doubling degeneracy is due to RðhÞ, C ~0. With the extended C9-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N. The Majorana mode[1,2,3,4] has attracted increasing attention in physics due to its potential applications in topological quantum information processing[5,6,7]. In the Ref. 8, Lee and Wilczek presented a new operator C that provided the doubling degeneracy for the Hamiltonian formed by Majorana fermions to overcome the conceptional incompletion of the algebraic set for the Majorana model
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