With the eigenfunctional theory, we give a general exact expression of the local electron Green function in the Falicov-Kimball model, and apply it to study the correlation effects of the local electrons in one dimension. For the two local electrons case, the correlation exponent of the local electron Green function has weak even-odd oscillation with the distance between these two local electrons, and it approaches zero in the strong coupling limit. While, at half filling of the local electrons, the ground-state phase is complicated. When the conduction electron is near
0.5, the ground state configuration is the chessboard phase for a considerable range of
U∕t∗, and the correlation exponent increases from zero to a finite value as
U∕t∗ increases. When the conduction electron is far away from
0.5, the ground state configuration is the segregated phase, and the correlation exponent first increases and then jumps to zero when
U∕t∗ is larger than a finite value which is a function of
nc. Our results are compared with previous numerical simulations.
We study the effect of strong correlations on the zero-bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model (EAHM) on a square lattice. The EAHM has both on-site and nearest-neighbour interactions and randomly chosen site energies. We use a mean-field theory that incorporates strong correlations and treats the disorder potential exactly. We use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit, and the off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half-filling, and enhance the ZBA gap when the interaction is finite ranged.
We study the effect of strong correlations on the zero bias anomaly (ZBA) in disordered interacting systems. We focus on the two-dimensional extended Anderson-Hubbard model, which has both on-site and nearest-neighbor interactions on a square lattice. We use a variation of dynamical mean field theory in which the diagonal self-energy is solved self-consistently at each site on the lattice for each realization of the randomly-distributed disorder potential. Since the ZBA occurs in systems with both strong disorder and strong interactions, we use a simplified atomic-limit approximation for the diagonal inelastic self-energy that becomes exact in the large-disorder limit. The off-diagonal self-energy is treated within the Hartree-Fock approximation. The validity of these approximations is discussed in detail. We find that strong correlations have a significant effect on the ZBA at half filling, and enhance the Coulomb gap when the interaction is finite-ranged.
We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of $d=1+\ensuremath{\epsilon}$ $(\ensuremath{\epsilon}\ensuremath{\ll}1)$ dimensions is also mentioned.
In this paper we investigate effects of a lattice dimension on strongly correlated electronic systems at
T=0K. The model for numerical calculations is formalized in terms of the integral equations which were obtained previously for the half -- filled paramagnetic Hubbard model. The assumption that all relevant functions of the system have a magnitude dependence of momentus vectors makes ultimately possible treating a lattice dimension
D as an external parameter. We here submit for consideration the number of doubly occupied lattice sites, the electronic density of states, and the momentum distribution in electronic occupation numbers at
D=1,
D=2,
D=3