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Entanglement entropy and entanglement spectrum of triplet topological superconductors

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Ribeiro,  P.
Max Planck Institute for Chemical Physics of Solids, Max Planck Society;

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Citation

Oliveira, T. P., Ribeiro, P., & Sacramento, P. D. (2014). Entanglement entropy and entanglement spectrum of triplet topological superconductors. Journal of Physics: Condensed Matter, 26(42): 425702, pp. 1-11. doi:10.1088/0953-8984/26/42/425702.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-97CC-4
Abstract
We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.