We analyze the entanglement entropy, in real space, for the higher-dimensional integer quantum Hall effect on ${\mathbb{C}\mathbb{P}}^k$ (any even dimension) for Abelian and non-Abelian 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 non-Abelian. 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.

• Received 26 June 2020
• Accepted 8 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.025016

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Published by the American Physical Society