Entanglement entropy and Berezin-Toeplitz operators

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.

v2: substantial revision, applications added to determinantal processes associated to Bergman kernel

References in corpus (4)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Allowed charge transfers between coherent conductors driven by a time-dependent scatterer
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy

Cited by in corpus (24)

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• The boundary density profile of a Coulomb droplet. Freezing at the edge
• Partition functions of determinantal and Pfaffian Coulomb gases with radially symmetric potentials
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Geometric entanglement in integer quantum Hall states
• Exponential moments for disk counting statistics of random normal matrices in the critical regime
• Stability of the enhanced area law of the entanglement entropy
• Asymptotic growth of the local ground-state entropy of the ideal Fermi gas in a constant magnetic field
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Stability of a Szegő-type asymptotics
• Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric Kähler manifolds
• Linear statistics at the microscopic scale for the 2D Coulomb gas
• Charge functions for odd dimensional partitions
• Equilibrium measures for higher dimensional rotationally symmetric Riesz gases