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Entanglement entropies in free fermion gases for arbitrary dimension

We study the entanglement entropy of connected bipartitions in free fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Renyi entanglement entropies grow asymptotically as N^(1-1/d) ln N, with a prefactor that is analytically computed using the Widom conjecture both for periodic and open boundary conditions. The logarithmic correction to the power-law behavior is related to the area-law violation in lattice free fermions. These asymptotic large-N behaviors are checked against exact numerical calculations for N-particle systems.

preprint2011arXivOpen access
Pasquale CalabreseMihail MintchevEttore Vicari
cond-mat.stat-mechhep-thcond-mat.quant-gasquant-ph
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Pasquale CalabreseMihail MintchevEttore Vicari

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