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Phys. Rev. Lett. 96, 010404 (2006) [4 pages]

Violation of the Entropic Area Law for Fermions

Michael M. Wolf
Max-Planck-Institute for Quantum Optics, Hans-Kopfermann Strasse 1, 85748 Garching, Germany
Received 1 April 2005; published 12 January 2006

We investigate the scaling of the entanglement entropy in an infinite translational invariant fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. Thus, in contrast with analogous bosonic systems, the entropic area law is violated for fermions. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven that the presented scaling law holds whenever the Fermi surface is finite. This is, in particular, true for all ground states of Hamiltonians with finite range interactions.

©2006 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevLett.96.010404
DOI: 10.1103/PhysRevLett.96.010404
PACS: 03.65.Ud; 04.70.Dy; 05.30.Fk; 71.18.+y
  • 03.65.Ud
    Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
  • 04.70.Dy
    Quantum aspects of black holes, evaporation, thermodynamics
  • 05.30.Fk
    Fermion systems and electron gas (quantum statistical mechanics)
  • 71.18.+y
    Fermi surface: calculations and measurements; effective mass, -g factor
  • YEAR: 2006
KEYWORDS: Fermi surface, fermion systems, entropy, tight-binding calculations, quantum entanglement, black holes

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