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Entanglement entropy and entanglement spectrum of the Kitaev model
In this paper, we obtain an exact formula for the entanglement entropy of the
ground state and all excited states of the Kitaev model. Remarkably, the
entanglement entropy can be expressed in a simple separable form S=S_G+S_F,
with S_F the entanglement entropy of a free Majorana fermion system and S_G
that of a Z_2 gauge field. The Z_2 gauge field part contributes to the
universal "topological entanglement entropy" of the ground state while the
fermion part is responsible for the non-local entanglement carried by the Z_2
vortices (visons) in the non-Abelian phase. Our result also enables the
calculation of the entire entanglement spectrum and the more general Renyi
entropy of the Kitaev model. Based on our results we propose a new quantity to
characterize topologically ordered states--the capacity of entanglement, which
can distinguish the states with and without topologically protected gapless
entanglement spectrum.Comment: 4.0 pages + supplementary material, published version in Phys. Rev.
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