  We model quantum dot nanostructures using a one-dimensional system of two
interacting electrons. We show that strong and rapid variations may be induced
in the spatial entanglement by varying the nanostructure geometry. We
investigate the position-space information entropy as an indicator of the
entanglement in this system. We also consider the expectation value of the
Coulomb interaction and the ratio of this expectation to the expectation of the
confining potential and their link to the entanglement. We look at the first
derivative of the entanglement and the position-space information entropy to
infer information about a possible quantum phase transition.

Quantum Physics;Strongly Correlated Electrons