Dynamical entanglement entropy with angular momentum and U(1) charge
Dynamical entanglement entropy with angular momentum and U(1) charge
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DOI：
10.1007/jhep11(2013)052
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发表时间：
2013-06
影响因子：
5.4
通讯作者：
Paweł Caputa;G. Mandal;R. Sinha
中科院分区：
文献类型：
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作者：
Paweł Caputa;G. Mandal;R. Sinha
我们考虑了角动量和U(1)电荷存在下1+1维CFT的含时纠缠熵。在与纠缠间隔的长度相比较大的时间之后，与初始状态无关，EE饱和到宏正则熵。我们复制了由旋转的BTZ黑洞和平坦的U(1)连接组成的ADS对偶的CFT结果。全息EE不先验地依赖于U(1)电荷，而CFT EE依赖于电荷，这一明显的差异通过体应力张量和边界应力张量之间的电荷相关位移得到了解决。我们证明了对于较小的纠缠间隔，纠缠熵服从热力学第一定律，这是最近的猜测。场论中EE的饱和是由量子遍历的一种形式而来的；推导表明，它应该适用于任何维度的共形理论和大规模理论。
We consider time-dependent entanglement entropy (EE) for a 1+ 1 dimensional CFT in the presence of angular momentum and U (1) charge. The EE saturates, irrespective of the initial state, to the grand canonical entropy after a time large compared with the length of the entangling interval. We reproduce the CFT results from an AdS dual consisting of a spinning BTZ black hole and a flat U (1) connection. The apparent discrepancy that the holographic EE does not a priori depend on the U (1) charge while the CFT EE does, is resolved by the charge-dependent shift between the bulk and boundary stress tensors. We show that for small entangling intervals, the entanglement entropy obeys the first law of thermodynamics, as conjectured recently. The saturation of the EE in the field theory is shown to follow from a version of quantum ergodicity; the derivation indicates that it should hold for conformal as well as massive theories in any number of dimensions.