Entanglement Entropy and Entanglement Spectrum of the Kitaev Model

被引:194
作者
Yao, Hong [1 ,2 ]
Qi, Xiao-Liang [3 ,4 ]
机构
[1] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA
[2] Univ Calif Berkeley, Lawrence Berkeley Lab, Div Mat Sci, Berkeley, CA 94720 USA
[3] Univ Calif Santa Barbara, Stn Q, Santa Barbara, CA 93106 USA
[4] Stanford Univ, Dept Phys, Stanford, CA 94305 USA
关键词
QUANTUM COMPUTATION; ANYONS; SUPERCONDUCTIVITY;
D O I
10.1103/PhysRevLett.105.080501
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 SG 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-the capacity of entanglement, which can distinguish the states with and without topologically protected gapless entanglement spectrum.
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页数:4
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