Abstract
A 1D model hamiltonian that is motivated by the recent discovery of the heavy-fermion behavior in the cuprates of the $Nd_2CuO_4$ type is studied. It consists of $t-J$ interacting conduction electrons coupled to a lattice of localized spins through a Kondo exchange term $J_K$. Exact diagonalization and density matrix renormalization group methods 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-filling$,$ it is shown that, at strong $J_K$% , the ground state is an unsaturated ferromagnet . At weak $J_K$ the system is in a paramagnetic phase with enhanced RKKY correlations. The importance of self-screening of the local moments in the depletion regime is discussed. We argue that these findings transcend the specifics of the model.
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