Geometry induced entanglement transitions in nanostructures

We model quantum dotnanostructures 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 nanostructuregeometry. We investigate the position-space informationentropy 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 informationentropy to infer information about a possible quantum phase transition.