We give a comprehensive analysis of the singular dynamics and of the low-energy fixed point of one-channel impurity s-d models with ferromagnetic and underscreened antiferromagnetic couplings. We use the numerical renormalization group (NRG) to perform calculations at T = 0. The spectral densities of the one-electron Green's functions and t-matrices are found to have very sharp cusps at the Fermi level (ω = 0), but do not diverge. The approach of the Fermi level is governed by terms proportional to 1/ ln 2 (ω/T0) as ω → 0. The scaled NRG energy levels show a slow convergence as 1/(N + C) to their fixed point values, where N is the iteration number and C is a constant dependent on the coupling J from which the low energy scale T0 can be deduced. We calculate also the dynamical spin susceptibility, and the elastic and inelastic scattering cross-sections as a function of ω. The inelastic scattering goes to zero as ω → 0, as expected for a Fermi liquid, but anomalously slowly compared to the fully screened case. We obtain the asymptotic forms for the phase shifts for elastic scattering of the quasiparticles in the high-spin and low-spin channels.

We present results on the dynamical correlation functions of the particle-hole symmetric HolsteinHubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propagator shows a characteristic softening near the metal to bipolaronic transition but there is very little softening on the approach to the Mott transition.

PACS. 71.10.Fd -Lattice fermion models (Hubbard model, etc.). PACS. 71.30.+h -Metal-insulator transitions and other electronic transitions . PACS. 71.38.-k -Polarons and electron-phonon interactions (see also 63.20.Kr Phonon-electron interactions in lattices).Abstract. -We investigate metal-insulator transitions in the half-filled Holstein-Hubbard model as a function of the on-site electron-electron interaction U and the electron-phonon coupling g. We use several different numerical methods to calculate the phase diagram, the results of which are in excellent agreement. When the electron-electron interaction U is dominant the transition is to a Mott-insulator; when the electron-phonon interaction dominates, the transition is to a localised bipolaronic state. In the former case, the transition is always found to be second order. This is in contrast to the transition to the bipolaronic state, which is clearly first order for larger values of U . We also present results for the quasiparticle weight and the double-occupancy as function of U and g.c EDP Sciences

We show that quasiparticles in a magnetic field of arbitrary strength H can be described by field dependent parameters. We illustrate this approach in the case of an Anderson impurity model and use the numerical renormalization group (NRG) to calculate the renormalized parameters for the levels with spin σ,ε d,σ (H), resonance width∆(H) and the effective local quasiparticle interactioñ U (H). In the Kondo or strong correlation limit of the model the progressive de-renormalization of the quasiparticles can be followed as the magnetic field is increased. The low temperature behaviour, including the conductivity, in arbitrary magnetic field can be calculated in terms of the field dependent parameters using the renormalized perturbation expansion. Using the NRG the field dependence of the spectral density on higher scales is also calculated.

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator-to-superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum-free of spurious gaps-despite the fact that it formally breaks translation invariance. The phase diagram and the singleparticle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimensional dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.