Antiferromagnetism of almost localized fermions: Evolution from Slater-type to Mott-Hubbard gap

Abstract

We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made.

Electronic properties of correlated nanoscopic systems from the exact diagonalization combined with an ab initio approach

“…First, the system exhibits a gap, which is of the same magnitude (but not quite) as the magnetic (Slater) gap obtained in the Hartree-Fock approximation. Second, with the increasing R the magnetic gap evolves into the Hubbard gap, as in the infinite system [16]. The presence of the magnetic gap in a nanoscopic system may seem quite unexpected.…”

Unconventional Superconducting States of an Almost Localized Fermionic Liquid with Nonstandard Quasiparticles: Generalized Gutzwiller Approach

“…d 2 ≡ 0) and the following simplified form of the effective Hamiltonian (14), which in the renormalized mean-field form for H a = 0 iŝ…”

“…Second, the concept of an effective field induced by the correlations appeared for the first time in the slave--boson approach [14] and represents an additional feature to the Gutzwiller-ansatz approach. It can appear within the picture of correlated quasiparticle states naturally via constraints imposed by statistical consistency of the results [15], so it is of universal nature whenever the concept of renormalized mean-field Hamiltonian is introduced.…”

Metal-insulator transition and antiferromagnetism in the generalized Hubbard model: Treatment of correlation effects

“…Whereas the electron density in the model is fixed, the role of other parameters (Coulomb and direct exchange interaction strengths as well as hopping integrals configuration) should be discussed in detail. It is well known that in the weak-coupling limit MIT typically follows the Slater scenario originating from the AFM gap formation [17,18]. In terms of the renormalization-group loop expansion, the electron interaction can be generally decomposed in one-loop level as the sum of three channels: particle-particle (Cooper), direct and crossed (magnetic) particle-hole contributions [19].…”