  We investigate entanglement of strongly interacting fermions in spatially
inhomogeneous environments. To quantify entanglement in the presence of spatial
inhomogeneity, we propose a local-density approximation (LDA) to the
entanglement entropy, and a nested LDA scheme to evaluate the entanglement
entropy on inhomogeneous density profiles. These ideas are applied to models of
electrons in superlattice structures with different modulation patterns,
electrons in a metallic wire in the presence of impurities, and phase-separated
states in harmonically confined many-fermion systems, such as electrons in
quantum dots and atoms in optical traps. We find that the entanglement entropy
of inhomogeneous systems is strikingly different from that of homogeneous
systems.
