Relation of entanglement entropy and particle number fluctuations in one-dimensional Hubbard model

Entanglement has emerged as an important tool for understanding the properties of interacting quantum systems, but experimental measurements have been made only to a limited extent. It has been proposed that the entanglement entropy of free particles is closely related to particle number fluctuations that are more readily accessible experimentally. We study the relation between entanglement entropy and particle number fluctuations in interacting fermion systems. By using a self-consistent Hartree–Fock approximation, we find that entanglement entropy and particle number fluctuations have a linear relation with a well-defined proportionality coefficient even for interacting systems. Furthermore, the relation holds in the presence of random potentials. This strongly suggests that entanglement, like other physical properties such as particle number fluctuations, is governed by the correlation length.