We explore the effect of fluctuations for
T≥Tc in the 2-D negative Hubbard model within the framework of the selfconsistent T-matrix formalism, which goes beyond the BCS approximation and includes pair fluctuations. We enter the regime where correlations are important, namely,
U/t=−4.0, where
t denotes the hopping matrix element between nearest neighboors and
U is the strength of the on-site interaction. Our results include: 1) In comparison to the free case, the distribution function,
n(k), reveals considerable renormalization. This fact makes us conclude that the Fermi surface is blurred for correlated electron systems; 2) There is a pseudogap in the density of states,
N(ω), around the chemical potential,
μ; and 3) The real part of the T-matrix, at zero frequency and zero momentum, vs
T/t shows a divergence at a particular temperature. This last result shows that more approximate T-matrix calculations, extended to
T = 0 are meaningless.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the
(±π,0),
(0,±π) regions as the normal state pseudogap observed in the high-
Tc superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around
Q=(π,π) and the flatness of the band dispersion around the saddle point.
Low-density nuclear matter at finite temperature is considered representing the strong coupling situation of a highly correlated fermion system. One-particle self-energies and the density of states in the vicinity of the pairing transition point are presented. Within the Green function approach, model calculations are performed using the thermodynamic
T matrix in ladder approximation. As a main result the formation of a pseudogap in the level density near the critical temperature of the pairing phase transition has been found. It is shown that compared to mean-field approaches the scenario of the onset of the pairing transition is essentially changed if correlations are taken into account.
We study the attractive Hubbard model on the Lieb lattice to understand the normal state above the superconducting critical temperature in a flat band system. We use cluster dynamical mean-field theory to compute the two-particle susceptibilities with full quantum fluctuations included in the cluster. At interaction strengths lower than the hopping amplitude, we find that the normal state on the flat band shows insulating behavior stemming from the localization properties of the flat band. A flat-band enhanced pseudogap with a depleted spectral function arises at larger interactions.
The two-dimensional attractive Hubbard model is studied in the weak-to-intermediate-coupling regime by employing a nonperturbative approach. It is 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 Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime $(\ensuremath{\Elzxh}\ensuremath{\omega}<{k}_{B}T)$ of the two-dimensional system. With increasing temperature the spectral weight fills in the pseudogap instead of closing it, and the pseudogap appears earlier in the density of states than in the spectral function. Small temperature changes around
T∗ can modify the spectral weight over frequency scales much larger than temperature. Several qualitative results for the s-wave case should remain true for d-wave superconductors.