Linearity of holographic entanglement entropy
Linearity of holographic entanglement entropy
复制标题
全息纠缠熵的线性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Brian Swingle
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文献类型：
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作者：
Ahmed Almheiri;Xi Dong;Brian Swingle
我们考虑了全息CFTs中纠缠熵的主要贡献是否真的如Ryu-Takayanagi公式所建议的那样由线性算子的期望值给出的问题。我们调查这个属性通过计算纠缠熵，通过复制技巧，在状态的双重叠加宏观不同的几何形状，并发现它与评估的期望值的区域运营商在这样的状态是一致的。然而，我们发现，一旦叠加中的半经典态的数量在CFT的中心电荷中呈指数增长，这就失败了。此外，在某些这样的情况下，我们发现，选择表面上评估的面积运算符取决于整个CFT的密度矩阵。这种非线性是通过Ryu-Takayanagi的同调处方在本体中实施的。因此，我们得出结论，同源约束是不是一个线性性质的CFT。我们还讨论了存在的“熵运营商”在一般系统中有大量的自由度。
A bstractWe consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.