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Entanglement entropy and entanglement spectrum of the Kitaev model

Jan 7, 2010

Published in:

Phys.Rev.Lett. 105 (2010) 8, 080501

Published: Aug 16, 2010

e-Print:

1001.1165 [cond-mat.str-el]

DOI:

10.1103/PhysRevLett.105.080501

View in:

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Abstract: (APS)

In this Letter, 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 nonlocal 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\char22{}the capacity of entanglement, which can distinguish the states with and without topologically protected gapless entanglement spectrum.

Note:

4.0 pages + supplementary material, published version in Phys. Rev. Lett

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