Strongly correlated spin-phonon systems: A scenario for heavy fermions

A lattice of localized spins, coupled to phonons, is considered. It is shown that in a certain range of coupling constants a nontrivial nonmagnetic ground state of the system can arise, where the spins are screened by the phonons. In this state, groups of an even number of spins form singlet clusters, the spins within each cluster being strongly coupled to each other due to the exchange of phonons. This is a purely quantum phenomenon: average lattice displacements are zero, while amplitudes of zero quantum vibrations within the clusters are enhanced; the effect vanishes in the limit of classical spins. The clusters may, in principle, form either a crystal or quantum liquid. The collective screening of spins by phonons is a nonperturbative effect: it takes place only if the coupling constant exceeds a certain threshold. We have found the ground state exactly for a specific model with a highly symmetric Hamiltonian and discussed corrections to our solution due to variations of the Hamiltonian. The thermodynamics of the system is found. Applications to the physics of heavy-fermion compounds are discussed.