Exact relations between particle fluctuations and entanglement in Fermi gases

Details Exact relations between particle fluctuations and entanglement in Fermi gases Exact relations between particle fluctuations and entanglement in Fermi gases

2011-11-21

arxiv.org/abs/1111.4836v3

EPL 98, 20003 (2012)

Physics

Condensed Matter

Statistical Mechanics

6 pages

Scientific paper

We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Renyi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.

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