Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions

Details Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions

2006-02-11

arxiv.org/abs/quant-ph/0602094v1

Phys Rev B 74, 073103 (2006)

Physics

Quantum Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevB.74.073103

Exactly solving a spinless fermionic system in two and three dimensions, we investigate the scaling behavior of the block entropy in critical and non-critical phases. The scaling of the block entropy crucially depends on the nature of the excitation spectrum of the system and on the topology of the Fermi surface. Noticeably, in the critical phases the scaling violates the area law and acquires a logarithmic correction \emph{only} when a well defined Fermi surface exists in the system. When the area law is violated, we accurately verify a conjecture for the prefactor of the logarithmic correction, proposed by D. Gioev and I. Klich [quant-ph/0504151].

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