Entanglement from density measurements: analytical density-functional for the entanglement of strongly correlated fermions

Abstract

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model, by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations -- which includes reproducing subtle signatures of the particle density stages -- shows that our density-functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, at contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.

6 pages, 3 figures

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• Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics
• Entanglement and exotic superfluidity in spin-imbalanced lattices
• Mott-Anderson Metal-Insulator Transitions from Entanglement
• Entanglement enhancement in spatially inhomogeneous many-body systems
• Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids
• Metric-space approach for distinguishing quantum phase transitions in spin-imbalanced systems
• Spin entanglement in atoms and molecules
• Entanglement in disordered superfluids: the impact of density, interaction and harmonic confinement on the Superconductor-Insulator transition
• Effects of Temperature and Magnetization on the Mott-Anderson Physics in one-dimensional Disordered Systems
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Work statistics and Entanglement across the fermionic superfluid-insulator transition
• Glassy disorder-induced effects in noisy dynamics of Bose-Hubbard and Fermi-Hubbard systems
• Genuine multipartite entanglement from many-electron systems
• Spins extracted from fermionic states and their entanglement properties
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains