A one-dimensional model Hamiltonian that is motivated by the recent di
scovery of the heavy-fermion behavior in the cuprates of the Nd2Cu4 ty
pe is studied. It consists of t-J interacting conduction electrons cou
pled to a lattice of localized spins through a Kondo exchange term J(K
). Exact diagonalization and density matrix renormalization-group meth
ods are used. The latter method is generalized to arbitrary densities.
At half filling, a spin gap opens for all J(K)>0. Away from half fill
ing It is shown that, at strong J(K), the ground state is an unsaturat
ed ferromagnet. At weak JK the system is in a paramagnetic phase with
enhanced Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations. The import
ance of self-screening of the local moments in the depletion regime is
discussed. We argue that these findings transcend the specifics of th
e model.