The density-matrix renormalization group method is used to study the three-band zigzag ladder model that simulates the electronic state of the t 2g -orbital system of the double string of the edge-shared CrO 6 octahedra in the half-metallic ferromagnet K 2 Cr 8 O 16 . The saturated ferromagnetism caused by the double-exchange mechanism is thereby demonstrated. We also use the Lanczos exact-diagonalization technique on small clusters to study the two Hubbard chains coupled with the ferromagnetic exchange interaction, whereby we consider the nonquasiparticle states in the half-metallic ferromagnet that appear in the single-particle spectral function.
The occurrence of retarded (with glue) and unretarded (without glue) pairing is thoroughly discussed in cuprates. We analyze some aspects of this problem in the context of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model in a large-
N approximation. When
1/N renormalizations are neglected the mean-field result is recovered, where the unretarded
d-wave superconducting pairing triggered by the spin-exchange interaction
J is obtained. However, the presence of a nonnegligible nearest-neighbors Coulomb interaction
V(q) kills superconductivity. If the non-double-occupancy constraint and its fluctuations are considered, the situation changes drastically. In this case,
V(q) is screened making
d-wave superconductivity very robust. In addition, we show that the early proposal for the presence of an unretarded pairing contribution triggered by the spin-exchange interaction
J can be discussed in this context.