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arXiv:1209.3268 · Physical Review A

Entanglement enhancement in spatially inhomogeneous many-body systems

Tobias Brünner, Erich Runge, Andreas Buchleitner, V. V. França

Published Mar 11, 2013• 10 citations
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Abstract

We investigate the effects of spatial inhomogeneities on the entanglement of modes of strongly correlated systems in the framework of small Fermi-Hubbard chains. We find regimes where entanglement is strongly enhanced by the presence of inhomogeneities. This contrasts with recent reports of entanglement destruction due to inhomogeneities. We further study this phenomenon using concepts of density functional theory and, thus, provide a general recipe for the prediction of entanglement enhancement in nanostructures. We find enhancement of up to $\ensuremath{\sim}27%$, as compared to impurity-free chains.

DOI
10.1103/physreva.87.032311

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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.
We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential vi{v}_{i}vi​ can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction Ui{U}_{i}Ui​. Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for a reexamination of model calculations assuming spatial homogeneity.
We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement entropy, and a nested LDA scheme to evaluate the entanglement entropy on inhomogeneous density profiles. These ideas are applied to models of electrons in superlattice structures with different modulation patterns, electrons in a metallic wire in the presence of impurities, and phase-separated states in harmonically confined many-fermion systems, such as electrons in quantum dots and atoms in optical traps. We find that the entanglement entropy of inhomogeneous systems is strikingly different from that of homogeneous systems.
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