  In this work, we study the numerical optimization of nearest-neighbor
concurrence of bipartite one and two dimensional lattices, as well as non
bipartite two dimensional lattices. These systems are described in the
framework of a tight-binding Hamiltonian while the optimization of concurrence
was performed using genetic algorithms. Our results show that the concurrence
of the optimized lattice structures is considerably higher than that of non
optimized systems. In the case of one dimensional chains the concurrence is
maximized when the system begins to dimerize, i.e. it undergoes a structural
phase transition (Peierls distortion). This result is consistent with the idea
that entanglement is maximal or shows a singularity near quantum phase
transitions and that quantum entanglement cannot be freely shared between many
objects (monogamy property). Moreover, the optimization of concurrence in
two-dimensional bipartite and non bipartite lattices is achieved when the
structures break into smaller subsystems, which are arranged in geometrically
distinguishable configurations. This behavior is again related to the monogamy
property.
