We compare calculations based on the dynamical mean-field theory of the Hubbard model with the infrared spectral weight $W(\ensuremath{\Omega},T)$ of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ and other cuprates. Without using fitting parameters we show that most of the anomalies found in $W(\ensuremath{\Omega},T)$ with respect to normal metals, including the existence of two different energy scales for the doping and the
T dependence of $W(\ensuremath{\Omega},T)$, can be ascribed to strong correlation effects.
When a van Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a nonanalytic contribution. This invalidates basic assumptions of Fermi liquid theory and within treatments based on perturbation theory leads to a non-Fermi liquid self-energy and transport properties. Such anomalies are shown to also occur in the strongly correlated metallic state within dynamical mean-field theory. We consider the Hubbard model on a two-dimensional square lattice with nearest- and next-nearest-neighbor hoppings within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scale
T0 an unusual maximum emerges in the imaginary part of the self-energy which is renormalized toward the Fermi level for finite doping. At zero temperature this double-well structure is suppressed but an anomalous energy dependence of the self-energy remains. For the frustrated Hubbard model on the square lattice with next-nearest-neighbor hopping, the presence of the van Hove singularity changes the asymptotic low-temperature behavior of the resistivity from a Fermi liquid to non-Fermi liquid dependency as function of doping. The results of this work are discussed regarding their relevance for high-temperature cuprate superconductors.
We discuss the problem of a possible “violation” of the optical sum rule in the normal (nonsuperconducting) state of strongly correlated electronic systems, using our recently proposed DMFT + Σ approach applied to two typical models: the “hot spot” model of the pseudogap state and the disordered Anderson-Hubbard model. We explicitly demonstrate that the general Kubo single-band sum rule is satisfied for both models, but the optical integral itself is in general dependent on temperature and characteristic parameters, such as the pseudogap width, correlation strength, and disorder scattering, leading to an effective “violation” of the optical sum rule, which may be observed in experiments.
Recent experiments revealed a striking asymmetry in the phase diagram of the high temperature cuprate superconductors. The correlation effect seems strong in the hole-doped systems and weak in the electron-doped systems. On the other hand, a recent theoretical study shows that the interaction strengths (the Hubbard U) are comparable in these systems. Therefore, it is difficult to explain this asymmetry by their interaction strengths. Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using the dynamical mean field theory. We find the difference in the "visibility" of the strong correlation effect between the hole- and electron-doped systems. This can explain the electron-hole asymmetry of the correlation strength without introducing the difference in the interaction strength.
A systematic study of optical and transport properties of the Hubbard model, based on the Metzner-Vollhardt dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one) and also compare qualitatively with many anomalous transport features of the high-T c cuprates. This anomalous behaviour of the normal-state properties is traced to a ‘collective single-band Kondo effect’, in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-
Tc superconductors. In particular, the relationship between the number
n of CuO
2 layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature
Tcopt is intriguing. As experimentally observed in layered cuprates,
Tcopt increases when
n is increased, up to
n=3, and, then, decreases for larger
n. However, the mechanism behind the
n dependence of
Tcopt remains elusive although there have been many studies on the
n dependence. In this paper, we studied a bilayer
t-
t′ Hubbard model to clarify the effects of the adjacent CuO
2 layers on the stability of the superconductivity by using a many-variable variational Monte Carlo method. We calculate the superconducting correlation at long distance and zero temperature, and the amplitude of the superconducting gap functions estimated from the momentum distribution as the observables correlated with
Tcopt. It is found that the in-plane superconducting correlation is not enhanced in comparison with that in the single-layer
t-
t′ Hubbard model. The superconducting correlations of the bilayer Hamiltonian are significantly small in the overdoped region in comparison with those of single-layer Hamiltonian, which is attributed to the van Hove singularity. In addition, we found that the amplitude of the superconducting gap functions is also similar in both the single-layer and bilayer
t-
t′ Hubbard model at the optimal doping. Therefore, we conclude that the adjacent Hubbard layers are not relevant to the enhancement of
Tcopt in the bilayer cuprates. Possible origins of the enhanced
Tcopt other than the adjacent layers are also discussed.