The 1D Ising model and topological order in the Kitaev chain

Abstract

We elaborate on the topological order in the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Delta=t, and chemical potential mu=0. In particular, we write out the explicit eigenstates of the open chain in terms of fermion operators, and show that the states as well as their energy eigenvalues are formally equivalent to those of an Ising chain. The models are physically different, as the topological order in the Kitaev chain corresponds to conventional order in the Ising model.

5 pages, no figures

References in corpus (4)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Possibility of direct observation of edge Majorana modes in quantum chains

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