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

We investigate by means of Dynamical Mean-Field Theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs in the attractive Hubbard model. We follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap $\Delta_0$ and the superfluid stiffness $D_S$, which controls the phase coherence. The BCS-BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two...

We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low energy Fermi liquid fixed point using the results of a numerical renormalization group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low density limit there is significant renormalization of the local quasiparticle interaction $\tilde U$, in agreement with estimates based on the two-particle scat...

We scrutinize the real-frequency structure of the self-energy in the superconducting state of the attractive Hubbard model within the dynamical mean-field theory. Within the strong-coupling superconducting phase which has been understood in terms of the Bose-Einstein condensation in the literature, we find two qualitatively different regions crossing over each other. In one region close to zero temperature, the self-energy depends on the frequency only weakly at low energy. O...

The BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is driven by the potentia...

Detailed analysis of the magnetic properties of the Hubbard model within dynamical mean-field theory (DMFT) is presented. Using a RPA-like decoupling of two-particle propagators we derive a universal form for susceptibilities, which captures essential aspects of localized and itinerant pictures. This expression is shown to be quantitatively valid whenever long-range coherence of particle-hole excitations can be neglected, as is the case in large parts of the phase diagram whe...

In the limit of infinite spatial dimensions a thermodynamically consistent theory of the strongly correlated electron systems, which is valid for arbitrary value of the Coulombic interaction ($U<\infty$), is built. For the Hubbard model the total auxiliary single-site problem exactly splits into four subspaces, which describe Fermi and non-Fermi liquid components. Such analytical approach allows to construct different thermodynamically consistent approximations: alloy-analogy...

We use non-equilibrium dynamical mean-field theory to demonstrate the existence of a critical interaction in the real-time dynamics of the Hubbard model after an interaction quench. The critical point is characterized by fast thermalization and separates weak-coupling and strong-coupling regimes in which the relaxation is delayed due to prethermalization on intermediate timescales. This dynamical phase transition should be observable in experiments on trapped fermionic atoms.

At zero temperature, two-site dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole ...

The ground state phase diagram of the two-dimensional attractive Hubbard model with population imbalance is explored using a mean field ansatz. A linear programming algorithm is used to identify the blocked states, such that the population imbalance can be imposed exactly. This allows to explore regions of the number-projected phase diagram that can not be obtained with the conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase of pairs wit...

It is shown that in the two-dimensional attractive Hubbard model, the mean-field phase transition is replaced by a renormalized classical regime of fluctuations where a pseudogap opens up in the single-particle spectral weight. It is argued that this pseudogap and precursors of the ordered state quasiparticles can occur only in strongly anisotropic quasi two-dimensional materials. This precursor phenomenon differs from preformed local pairs. Furthermore, while critical antife...