We analyze the entanglement entropy, in real space, for the higher dimensional integer quantum Hall effect on ${ℂ\mathbb{P}}^k$ (any even dimension) for abelian and nonabelian magnetic background fields. In the case of $\nu =1$ we perform a semiclassical calculation which gives the entropy as proportional to the phase-space area. This exhibits a certain universality in the sense that the proportionality constant is the same for any dimension and for any background, abelian or nonabelian. We also point out some distinct features in the profiles of the eigenfunctions of the two-point correlator that underline the difference in the value of entropies between $\nu =1$ and higher Landau levels. \end{titlepage} \setcounter{page}{2 …

中文翻译：

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二维和更高维整数量子霍尔效应的纠缠熵

对于高维整数量子霍尔效应，我们分析了真实空间中的纠缠熵 ${ℂ\mathbb{P}}^{ķ}$（任何偶数维）用于阿贝尔和非阿贝尔磁场背景场。如果是$\nu =\mathrm{1个}$我们执行了一个半经典的计算，该计算给出了与相空间面积成比例的熵。从比例常数对于任何维度以及任何背景（阿贝尔或非阿贝尔）相同的意义上来说，这表现出某种普遍性。我们还指出了两点相关器特征函数轮廓中的一些明显特征，这些特征突显了两点之间的熵值之间的差异。$\nu =\mathrm{1个}$和更高的Landau水平。\ end {titlepage} \ setcounter {page} {2…