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arXiv · 1803.03149

Entanglement entropy and Berezin-Toeplitz operators

L. Charles·B. Estienne
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Abstract

We consider Berezin-Toeplitz operators on compact Kahler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a consequence, we deduce the area law for the entanglement entropy of integer quantum Hall states. Another application is for the determinantal processes with correlation kernel the Bergman kernels of a positive line bundle : we prove that the number of points in a smooth domain is asymptotically normal.

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BibTeXRIS

L. Charles, B. Estienne. 2018-03-08. Entanglement entropy and Berezin-Toeplitz operators. https://doi.org/10.1007/s00220-019-03625-y

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