Entanglement, magnetism, and metal-insulator transitions in fermionic superlattices

We discuss how entanglement of strongly correlated fermions is influenced by a superlattice structure by considering a one-dimensional Hubbard superlattice, made up of a repeated pattern of L sub(U) repulsive sites followed by L sub(0) free sites. Lanczos diagonalization of lattices up to 24 sites is used to calculate the von Neumann entropy and the negativity. The breakdown of particle-hole symmetry broadens the maxima of the entropy in the underdoped region, while the entanglement in the overdoped region is crucially influenced by the nature of the magnetic state, with dips at densities corresponding to repulsive-layer singlets and to q = [pi] (in units of inverse unit cell length, L sub(U) + L sub(0)) spin-density waves. At these special densities, the system is either a Mott insulator or a "compressible insulator." We have also found that sites within the same repulsive layer (for L sub(U) > or = 2) are monogamically entangled with each other, which may provide a route to control entanglement simultaneously in different length scales.