Universality of quantum information in chaotic CFTs
Universality of quantum information in chaotic CFTs
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DOI：
10.1007/jhep03(2018)070
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发表时间：
2017-10
影响因子：
5.4
通讯作者：
Nima Lashkari;A. Dymarsky;Hong Liu
中科院分区：
文献类型：
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作者：
Nima Lashkari;A. Dymarsky;Hong Liu
研究了任意维混沌共形场理论中的本征态热化假设。假定局域ETH，当整个系统为能量本征态时，我们在无限体积极限下计算了有限大小的球形子系统的约化密度矩阵。这个约化的密度矩阵在迹距离上接近密度矩阵，我们称之为Eth密度矩阵，它独立于本征态的所有细节，除了它在整体对称性下的能量和电荷。在两维空间中，对于中心电荷值相同的所有理论，Eth密度矩阵是通用的。我们认为，Eth密度矩阵在迹距离上接近(微)正则系综约化密度矩阵。通过比较Eth密度矩阵的Von Neumann熵和低温极限下全息系统中黑洞的Von Neumann熵，我们在更高的维度上支持了这一论点。最后，我们将我们的分析推广到能量密度在空间中缓慢变化的相干态，并表明局域这样的态可以用Eth密度矩阵很好地描述。
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro) canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.