  We studied the ground state of alkaline-earth-metal atoms confined in
one-dimensional optical lattices with an effective hybridization generated by a
suitable laser field. This system is modeled by the periodic Anderson model
plus a quadratic confining potential, and we adopted the density-matrix
renormalization group to calculate its ground state. We found a one-to-one
correspondence between the local variance, the local von Neumann entropy, and
the on-site spin-spin correlation. For low global densities, we observed the
formation of local singlets between delocalized and localized atoms and found
Kondo spin liquid domains that can be tuned with the confining potential, the
hybridization, and the local repulsion. Band insulator, metallic, phase
separation, and Kondo spin liquid regions coexist in the ground state.
