The Hubbard model as an approximation to the entanglement in nanostructures

TL;DR

This paper assesses the effectiveness of the one-dimensional Hubbard model in approximating particle entanglement in quantum well systems, exploring interaction effects, analytical limits, and entanglement behavior.

Contribution

It introduces a comparison framework between quantum well entanglement and the Hubbard model, including analytical bounds and the influence of potential parameters.

Findings

Hubbard model approximates entanglement well under certain conditions

Identifies upper bounds for single-site entanglement in two-electron systems

Analyzes how interaction strength and potential shape affect entanglement maxima

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.