2014/09/11 by Li-Wei Yu, Yu, Li-Wei, Mo‐Lin Ge +1
Physics and Astronomy · #Advanced Condensed Matter Physics #Topological Materials and Phenomena #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1409.3396
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. \breveR(θ)-matrix. For 2-body interaction, \breveR(θ) 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 \breveR123-matrix, we thus show that the essence of the doubling degeneracy is due to [\breveR(θ), Γ]=0. 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.