Department of Physics, University of California, Berkeley, California 94720, USA.
Phys Rev Lett. 2010 Aug 20;105(8):080501. doi: 10.1103/PhysRevLett.105.080501. Epub 2010 Aug 16.
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 = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 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 Z2 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 st ates with and without topologically protected gapless entanglement spectrum.
在这封信中，我们得到了 Kitaev 模型的基态和所有激发态的纠缠熵的精确公式。值得注意的是，纠缠熵可以表示为一个简单可分的形式 S = SG + SF，其中 SF 是自由马约拉纳费米子系统的纠缠熵，SG 是 Z2 规范场的纠缠熵。Z2 规范场部分贡献了基态的通用“拓扑纠缠熵”，而费米子部分则负责非阿贝尔相中的 Z2 涡旋（幻子）携带的非局域纠缠。我们的结果还可以计算 Kitaev 模型的整个纠缠谱和更一般的 Renyi 熵。基于我们的结果，我们提出了一个新的量来表征拓扑有序态——纠缠容量，它可以区分具有和不具有拓扑保护无能隙纠缠谱的态。
