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Entanglement and fidelity in topological superconductors

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A p-wave superconductor, with Rashba spin-orbit coupling and a Zeeman term displays various topological phases that can be detected in various ways such as the Chern number or by gapless edge states. In this talk we use bulk and local quantum information methods to detect the transitions. We show that the von Neumann entropy, the entanglement spectrum, fidelity and the fidelity spectrum may be used to signal the transitions. The nature of the phases and their changes are clarified by the eigenvectors of the k-space reduced density matrix and by the eigenvectors of the k-fidelity operator. A signature of the various phase transitions between two points in the parameter space is encoded in the k-space fidelity operator. We also show that local entanglement entropy and the topological entanglement entropy also signal the topological transitions. We find that a derivative of the entanglement entropy shows approximate plateaus that are related to the Chern numbers. We also suggest that the topological entanglement entropy in a half-cylinder geometry is closely related to the number of edge states.

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