We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.

Raman experiments on the spin-Peierls compound CuGeO3 and the substituted (Cu1−x,Znx)GeO3 and Cu(Ge1−x,Gax)O3 compounds were performed in order to investigate the response of specific magnetic excitations of the one-dimensional spin-1/2 chain to spin anisotropies and substitution-induced disorder. In pure CuGeO3, in addition to normal phonon scattering which is not affected at all by the spin-Peierls transition, four types of magnetic scattering features were observed. Below TSP =14 K a singlet-triplet excitation at 30 cm −1 , two-magnon scattering from 30 to 227 cm −1 and folded phonon modes at 369 and 819 cm −1 were identified. They were assigned by their temperature dependence and lineshape. For temperatures between the spin-Peierls transition TSP and approximately 100 K a broad intensity maximum centered at 300 cm −1 is observed. The temperature dependence of this intensity is similar to the behavior of lattice fluctuations recently observed in an electron diffraction study. This scattering is attributed to dynamical spin-Peierls fluctuations of the weakly or non-static dimerized spin chain. 1 1

Key words Bethe lattice, frustration, dynamical mean-field theory, Green function.PACS 71.10.Fd, 71.27.+a Dedicated to Bernhard Mühlschlegel on the occasion of his 80th birthdayWe calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-selfintersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity which maps the problem onto the case of only nearestneighbor hopping. We find in particular that hopping between next-nearest neighbors leads to an asymmetric spectrum with additional van-Hove singularities.

We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.

The Hubbard model with unconstrained hopping of the particles on a lattice is solved exactly. It is shown that in this case the kinetic energy commutes with the interaction part, i.e. , the model is essentially trivial. The thermodynamics is worked out explicitly. One finds that the results of the quasichemical approximation for the occupation probability of lattice sites are exact for this model.The ground state is insulating at half-filling and U )0 and is conducting otherwise.