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.
|Autori:||Calabrese P; Mintchev M; Vicari E|
|Titolo:||Exact relations between particle fluctuations and entanglement in Fermi gases|
|Anno del prodotto:||2012|
|Digital Object Identifier (DOI):||10.1209/0295-5075/98/20003|
|Appare nelle tipologie:||1.1 Articolo in rivista|