Exact relations between particle fluctuations and entanglement in Fermi gases

TL;DR

This paper establishes exact mathematical relations between entanglement measures and particle number fluctuations in noninteracting Fermi gases, revealing that entanglement entropy scales with particle variance and can be experimentally estimated.

Contribution

It derives exact relations linking entanglement entropies and particle fluctuations in Fermi gases, including large-N asymptotics and impurity effects, with implications for experimental measurements.

Findings

Entanglement entropy asymptotically proportional to particle number variance.

Particle cumulant expansion converges for all integer-order Renyi entropies except von Neumann.

First few cumulants suffice for good entanglement approximation.

Abstract

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.