Entanglement in disordered superfluids: The impact of density, interaction and harmonic confinement on the Superconductor-Insulator transition

We investigate the influence of density, interaction and harmonic confinement on the superfluid to insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. We quantify the ground-state single-site entanglement via density-functional theory calculations of the linear entropy. We analyze the critical concentration C-C at which the fully-localized state - a special type of localization, with null entanglement - emerges. We find that C-C is independent on the interaction, but demands a minimum disorder strength to occur. We then derive analytic relations for C-C as a function of the average particle density for attractive and repulsive disorder. Our results reveal that weak harmonic confinement does not impact the properties of the fully-localized state, which occurs at the same C-C, but stronger confinements may lead the system from the fully-localized state to the ordinary localization. (C) 2019 Elsevier B.V. All rights reserved.