Dynamical mean-field theory for the normal phase of the attractive Hubbard model

One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak coupling regime using the non-selfconsistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real frequency axis. For temperatures sufficiently close to the superconducting transition temperature a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing impor...

The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. While analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impr...

The low-energy physics of the one-dimensional Pair-Hopping (PH) and attractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenged this idea and predicted the existence of a phase transition at half-filling and finite positive coupling for the pair-hopping model. We re-examine the controversy by making systematic comparisons between numerical results obtained for the PH and attractive Hubbard mod...

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in ...

BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We fin...

We report on a fully self-consistent determination of a phase transition to a superconducting state in a conserving approximation. The transition temperature calculated for a two-dimensional Hubbard model with an attractive interaction in the fluctuation exchange approximation agrees with quantum Monte Carlo calculations. The temperature dependences of the superfluid density and of the specific heat near the transition temperature indicate that the phase transition in this mo...

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fracti...

The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte ...

We present the results of numerical studies of superconductivity and antiferromagnetism in a strongly correlated electron system. To do this we construct a Hubbard model on a lattice of self-consistently embedded multi-site clusters by means of a dynamical mean-field theory in which intra-cluster dynamics is treated essentially exactly. We show that a class of characteristic features which have been seen in the excitation spectra of high-$T_{c}$ cuprates (e.g., pseudogap and ...

The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with Dynamical Mean Field Theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low-energy, while this reduction is not present at high energy. The renormalization of the electron-phonon co...