The Hubbard model as an approximation to the entanglement in nanostructures

Abstract

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 M 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.

arXiv comment9 pages, 6 figures, submitted to PRA.

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• Many-body effects on the thermodynamics of closed quantum systems
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• Testing density-functional approximations on a lattice and the limits of the related Hohenberg-Kohn-type theorem
• Melting a Hubbard dimer: benchmarks of `ALDA' for quantum thermodynamics
• Interspecies entanglement with impurity atoms in a lattice gas
• Metric-space approach for distinguishing quantum phase transitions in spin-imbalanced systems
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Pairwise quantum correlations in four-level quantum dot systems
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Characterizing Adiabaticity in Quantum Many-Body Systems at Finite Temperature
• Insights into Phase Transitions and Entanglement from Density Functional Theory
• Approximating quantum thermodynamic properties using DFT
• A $\pi$-shaped Quantum Device for Implementation of Bell States in Solid State Environment
• Spin-resolved Mott crossover and entanglement in the half-filled Hubbard model
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains