Abstract
We analyze the entanglement entropy, in real space, for the higher dimensional integer quantum Hall effect on ${\mathbb {CP}}^k$ (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.
Highlights
Entanglement has been used to explore properties of quantum states in a variety of condensed matter systems
For gapped two-dimensional systems, the leading order contribution to the entanglement entropy is proportional to the perimeter of the boundary separating the two subsystems, in particular S 1⁄4 cL þ γ þ Oð1=LÞ, where L is the length of the boundary, c is a nonuniversal coefficient and γ is a universal quantity called topological entanglement entropy [1]
The entanglement entropy in the case of integer quantum Hall states is amenable to analytical calculations due to the fact that the many-body ground state is given in terms of free fermions
Summary
Entanglement has been used to explore properties of quantum states in a variety of condensed matter systems. Entanglement calculations have been used to characterize various topologically ordered phases and further extract information on the edge properties of such systems [2,3,4,5,6,7,8] This is one of the key motivations for the study of entanglement entropy in the context of quantum Hall effect. The entanglement entropy in the case of integer quantum Hall states is amenable to analytical calculations due to the fact that the many-body ground state is given in terms of free fermions. The formulation of QHE on CPk for k > 1 displays two interesting features: higher dimensionality and the possibility of introducing both Abelian and non-Abelian magnetic fields In the latter case one deals with a manybody system of free fermions with internal degrees of freedom which is amenable to analytical calculations.
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