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arXiv:1007.5441 · Europhysics Letters (EPL)

Feasibility of approximating spatial and local entanglement in long-range interacting systems using the extended Hubbard model

J. P. Coe, V. V. França, Irene D’Amico

Published Jan 1, 2011• 21 citations
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Abstract

We investigate the extended Hubbard model as an approximation to the local and spatial entanglement of a one-dimensional chain of nanostructures where the particles interact via a long-range interaction represented by a "soft" Coulomb potential. In the process we design a protocol to calculate the particle-particle spatial entanglement for the Hubbard model and show that, in striking contrast with the loss of spatial degrees of freedom, the predictions are reasonably accurate. We also compare results for the local entanglement with previous results found using a contact interaction ( Coe J. P. et al ., Phys. Rev. A , 81 (2010) 052321 ) and show that while the extended Hubbard model recovers a better agreement with the entanglement of a long-range interacting system, there remain realistic parameter regions where it fails to predict the quantitative and qualitative behaviour of the entanglement in the nanostructure system.

DOI
10.1209/0295-5075/93/10001

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We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in MMM wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement.
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We consider the position-space information and linear entropies as proxy measures to the average single-site entanglement–quantified using the von Neumann entropy–of the one-dimensional Hubbard model and of a one-dimensional nanostructure system comprised of an array of quantum-dots. Spatial entanglement in the quantum-dot system is also investigated via the three entropies. We appraise the use of the possible proxy measures in the Hubbard model as an approximation to their use for the nanostructure system.
Using extended dynamical mean-field theory and its combination with the GWGWGW approximation, we compute the phase diagrams and local spectral functions of the single-band extended Hubbard model on the square and simple cubic lattices, considering long-range interactions up to the third nearest neighbors. The longer-range interactions shift the boundaries between the metallic, charge-ordered insulating, and Mott insulating phases, and lead to characteristic changes in the screening modes and local spectral functions. Momentum-dependent self-energy contributions enhance the correlation effects and thus compete with the additional screening effect from longer-range Coulomb interactions. Our results suggest that the influence of longer-range intersite interactions is significant, and that these effects deserve attention in realistic studies of correlated materials.