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The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension.
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1961
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A. M. Tsvelik, “Majorana fermion realization of a two-channel Kondo effect in a junction of three quantum Ising chains,” Phys. Rev. Lett. 110
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Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, and Matthew P. A. Fisher, “Non-Abelian statistics and topological quantum information processing in 1D wire networks,” Nat. Phys. 7
2011
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James D. Whitfield, Jacob Biamonte, and Alán Aspuru-Guzik, “Simulation of electronic structure Hamiltonians using quantum computers,” Molecular Physics 109
2011
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Lukasz Fidkowski and Alexei Kitaev, “Topological phases of fermions in one dimension,” Phys. Rev. B 83
2011
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The Majorana operators are connected to the usual fermionic creation and annihilation operators c † , c c^{\dagger},c in the following way: γ α ( 2 j − 1 ) = c α ( j ) + c α † ( j ) \gamma_{\alpha}(2j-1)=c_{\alpha}(j)+c_{\alpha}^{\dagger}(j) and γ α ( 2 j ) = − i [ c α ( j ) − c α † ( j ) ] \gamma_{\alpha}(2j)=-\mathrm{i}\left[c_{\alpha}(j)-c_{\alpha}^{\dagger}(j)\right]
Cited in the paper.
2015
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Stefan Backens, Alexander Shnirman, Yuriy Makhlin, Yuval Gefen, Johan E. Mooij, and Gerd Schön, “Emulating Majorana fermions and their braiding by Ising spin chains,” Phys. Rev. B 96
2017
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R. Aguado, “Majorana quasiparticles in condensed matter,” Riv. Nuovo Cimento 40
2017
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