For a system consisting of two interacting subsystems, effective Hamiltonians for one subsystem are usually constructed by integrating out the degrees of freedom of the second subsystem. In contrast to usual treatments, our method for deriving effective Hamiltonians is based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other approaches. The formalism applies for any temperature. Our method is based on a matrix formulation in the framework of a recently introduced cumulantprojection method. This method allows the treatment of strongly correlated systems, where conventional diagrammatic techniques are difficult to apply. The relation with perturbation theory is also shown. As a simple application we discuss the small polaron problem. Evaluating the one-electron dispersion relation in the strong-coupling case shows good agreement with recent results from exact Lanczos diagonalization. Our method has substantial advantages over perturbation theory.
We present a positive-muon spectroscopy study of the cubic Kondo lattice , where the crystal-field splittings of the ion amount to a few tens of K. The transition from the paramagnetic to the antiferromagnetic state is detected at . The zero-field data provide evidence of an unusual temperature dependence of the mean nuclear dipole field at the muon site. The longitudinal relaxation rate as well as the published quasi-elastic neutron linewidth, both recorded far into the paramagnetic region (, are analysed in detail. We show that the classical kf exchange interaction cannot explain the observed thermal variation of the dynamical and neutron widths. We perform a calculation of the 4f excitation spectra using the expansion, applied to the Anderson one-impurity Hamiltonian in the non-crossing approximation (NCA), in the presence of crystal-field splittings, and compare the results with the observed thermal variations of the dynamical widths. Whereas the NCA reasonably explains the neutron measurements, it strongly overestimates the low-temperature width. We discuss different possible reasons for this discrepancy.
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