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

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.042311· OSTI ID:21544578

Franca, Vivian V ^[1]; D'Amico, Irene ^[2]

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1. Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder Strasse 3, D-79104 Freiburg (Germany)
2. Department of Physics, University of York, York YO10 5DD (United Kingdom)

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, in 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.

• OSTI ID: 21544578
• Journal Information: Physical Review. A, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevA.83.042311; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
ATOMS
DENSITY
DENSITY FUNCTIONAL METHOD
ENTROPY
FERMIONS
HUBBARD MODEL
ONE-DIMENSIONAL CALCULATIONS
QUANTUM ENTANGLEMENT
SUPERLATTICES
CALCULATION METHODS
CRYSTAL MODELS
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
VARIATIONAL METHODS