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

TL;DR

This paper assesses the extended Hubbard model's ability to approximate spatial and local entanglement in long-range interacting nanostructures, finding it reasonably accurate but with notable limitations in certain parameter regimes.

Contribution

It introduces a protocol to compute particle-particle spatial entanglement within the Hubbard model and compares its predictions to long-range interacting systems.

Findings

Hubbard model reasonably approximates spatial entanglement

Extended Hubbard model improves agreement over contact interaction models

Limitations exist in certain parameter regions where predictions fail

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 (PRA, 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.