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Title: 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, 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.

Authors:
 [1];  [2]
  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)
Publication Date:
OSTI Identifier:
21544578
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.83.042311; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Franca, Vivian V, Capes Foundation, Ministry of Education of Brazil, Caixa Postal 250, 70040-020 Brasilia, and D'Amico, Irene. Entanglement from density measurements: Analytical density functional for the entanglement of strongly correlated fermions. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.042311.
Franca, Vivian V, Capes Foundation, Ministry of Education of Brazil, Caixa Postal 250, 70040-020 Brasilia, & D'Amico, Irene. Entanglement from density measurements: Analytical density functional for the entanglement of strongly correlated fermions. United States. https://doi.org/10.1103/PHYSREVA.83.042311
Franca, Vivian V, Capes Foundation, Ministry of Education of Brazil, Caixa Postal 250, 70040-020 Brasilia, and D'Amico, Irene. Fri . "Entanglement from density measurements: Analytical density functional for the entanglement of strongly correlated fermions". United States. https://doi.org/10.1103/PHYSREVA.83.042311.
@article{osti_21544578,
title = {Entanglement from density measurements: Analytical density functional for the entanglement of strongly correlated fermions},
author = {Franca, Vivian V and Capes Foundation, Ministry of Education of Brazil, Caixa Postal 250, 70040-020 Brasilia and D'Amico, Irene},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.83.042311},
url = {https://www.osti.gov/biblio/21544578}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 83,
place = {United States},
year = {2011},
month = {4}
}