Abstract:
In a recent Letter, Peets, et al. measured the x-ray intensity at the oxygen K-edge in overdoped La$_{2-x}$Sr$_x$CuO$_{4\pm\delta}$ (LSCO) and Tl$_2$Ba$_2$CuO$_{6+\delta}$. They claimed that, unlike the underdoped samples of LSCO and YBa$_2$Cu$_3$O$_x$ in which the integrated intensity increases at least linearly with doping, it saturates abruptly for a hole count exceeding $x\approx 0.23$. They interpreted the saturation as a breakdown of the 1-band Hubbard model in the cuprates. However, we show that their results are in quantitative agreement with the 1-band Hubbard model.

Abstract:
We study states in the superconducting gap induced by magnetic impurities using self-consistent quantum Monte Carlo with maximum entropy and formally exact analytic continuation methods. The magnetic impurity susceptibility has different characteristics for $T_{0} \alt T_{c0}$ and $T_{0} \agt T_{c0}$ ($T_{0}$: Kondo temperature, $T_{c0}$: superconducting transition temperature) due to the crossover between a doublet and a singlet ground state. We systematically study the location and the weight of the gap states and the gap parameter as a function of $T_{0}/T_{c0}$ and the concentration of the impurities.

Abstract:
The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping whereas the AF susceptibility at intermediate doping increases with decreasing phonon frequency $\omega_0$. This IE stems from increased polaronic effects with decreasing $\omega_0$. A larger IE at smaller doping occurs due to stronger polaronic effects determined by the interplay of the EP interaction with stronger AF correlations. The IE of the Hubbard-Holstein model exhibits many similarities with the IE measured in cuprate superconductors.

Abstract:
Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are considered. The strong correlation between excitations on parallel neighboring bonds suggests bond singlet dimerization. The suppression of divergence for $n< \approx 0.78$ implies that tor these model parameters this is quantum critical point which separates the unconventional pseudogap region characterized by bond order from a conventional Fermi liquid.

Abstract:
The Holstein-Hubbard model is examined in the limit of infinite dimensions. Conventional folklore states that charge-density-wave (CDW) order is more strongly affected by Coulomb repulsion than superconducting order because of the pseudopotential effect. We find that both incommensurate CDW and superconducting phases are stabilized by the Coulomb repulsion, but, surprisingly, the commensurate CDW transition temperature is more robust than the superconducting transition temperature. This puzzling feature is resolved by a detailed analysis of perturbation theory.

Abstract:
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out thru fourth order for the Hubbard model. The self energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half filling because the iterated perturbation theory is not a conserving approximation. (REPLACED WITH UUENCODED FIGURES AT THE END. THE TEXT IS UNCHANGED)

Abstract:
The electron-phonon interaction corresponding to the Holstein model (with Coulomb repulsion) is simulated in infinite dimensions using a novel quantum Monte Carlo algorithm. The thermodynamic phase diagram includes commensurate charge-density-wave phases, incommensurate charge-density-wave phases, and superconductivity. The crossover from a weak-coupling picture (where pairs both form and condense at $T_c$) to a strong-coupling picture (where preformed pairs condense at $T_c$) is illustrated with the onset of a double-well structure in the effective phonon potential.

Abstract:
The competition between commensurate and incommensurate spin-density-wave phases in the infinite-dimensional single-band Hubbard model is examined with quantum Monte Carlo simulation and strong and weak coupling approximations. Quantum fluctuations modify the weak-coupling phase diagram by factors of order unity and produce remarkable agreement with the quantum Monte Carlo data, but strong-coupling theories (that map onto effective Falicov-Kimball models) display pathological behavior. The single-band model can be used to describe much of the experimental data in Cr and its dilute alloys with V and Mn.

Abstract:
The phase diagram of the two-channel Kondo lattice model is examined with a Quantum Monte Carlo simulation in the limit of infinite dimensions. Commensurate (and incommensurate) antiferromagnetic and superconducting states are found. The antiferromagnetic transition is very weak and continuous; whereas the superconducting transition is discontinuous to an odd-frequency channel-singlet and spin-singlet pairing state.

Abstract:
We employ dynamical mean-field theory to identify the materials properties that optimize Tc for a generalized double-exchange (DE) model. We reach the surprising conclusion that Tc achieves a maximum when the band angular momentum j equals 3/2 and when the masses in the 1/2 and 3/2 sub-bands are equal. However, we also find that Tc is significantly reduced as the ratio of the masses decreases from one. Consequently, the search for dilute magnetic semiconductors (DMS) materials with high Tc should proceed on two fronts. In semiconductors with p bands, such as the currently studied Mn-doped Ge and GaAs semiconductors, Tc may be optimized by tuning the band masses through strain engineering or artificial nanostructures. On the other hand, semiconductors with s or d bands with nearly equal effective masses might prove to have higher Tc's than p-band materials with disparate effective masses.