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Entanglement Entropy and Berezin–Toeplitz Operators

  • Laurent CharlesEmail author
  • Benoit Estienne
Article
  • 24 Downloads

Abstract

We consider Berezin–Toeplitz operators on compact Kähler 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.

Notes

Acknowledgements

The authors would like to express their warm gratitude to Benoît Douçot for bringing about this collaboration and for pointing out that the IQH entanglement entropy can be computed in terms of the spectrum of a convenient Toeplitz operator. B.E. also thanks Nicolas Regnault and Semyon Klevtsov for valuable discussions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu-Paris Rive GaucheIMJ-PRG, Sorbonne UniversitéParisFrance
  2. 2.Laboratoire de Physique Théorique et Hautes ÉnergiesLPTHE, Sorbonne UniversitéParisFrance

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