  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.
