论文标题
关于保姆空间的纠缠范围的评论
Comments on the Entanglement Spectrum of de Sitter Space
论文作者
论文摘要
我们认为Schwarzschild-De Sitter黑洞熵公式并不意味着De Sitter空间的真空密度矩阵的纠缠光谱是平坦的。 Specifically, we show that the expectation value of a random projection operator of dimension $d\gg 1$, on a Hilbert space of dimension $D\gg d$ and in a density matrix $ρ= e^{-K}$ with strictly positive spectrum, is $\frac{d}{D}\left(1 + o（\ frac {1} {\ sqrt {d}}）\ right）$，与密度矩阵的频谱无关。此外，对于合适的光谱类别，渐近估计$ {\ rm tr}（ρk）\ sim {\ rm ln} \ d -o（1）$和$ {\ rm tr} [ρ（k- \ \ langle k \ rangle k \ rangle）^2] = a \ langle k \ langle k \ rangice n $ and $ rangibus $ ranguce。我们讨论一个简单的基质模型和预测系列，可以复制这种模块化的哈密顿量和SDS熵公式。
We argue that the Schwarzschild-de Sitter black hole entropy formula does not imply that the entanglement spectrum of the vacuum density matrix of de Sitter space is flat. Specifically, we show that the expectation value of a random projection operator of dimension $d\gg 1$, on a Hilbert space of dimension $D\gg d$ and in a density matrix $ρ= e^{-K}$ with strictly positive spectrum, is $\frac{d}{D}\left(1 + o(\frac{1}{\sqrt{d}})\right)$, independent of the spectrum of the density matrix. In addition, for a suitable class of spectra the asymptotic estimates ${\rm Tr} (ρK) \sim {\rm ln}\ D - o(1)$ and $ {\rm Tr} [ρ(K - \langle K\rangle)^2] = a \langle K \rangle$ are compatible for any order one constant $a$. We discuss a simple family of matrix models and projections that can replicate such modular Hamiltonians and the SdS entropy formula.
