Local moments coupled to a strongly correlated electron chain

A one-dimensional model Hamiltonian that is motivated by the recent discovery of the heavy-fermion behavior in the cuprates of the ${\mathrm{Nd}}_2$Cu${\mathrm{O}}_4$ 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 $J_K>0\mathrm{}$. 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 Ruderman-Kittel-Kasuya-Yosida (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.