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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.
