Itinerant antiferromagnetism of correlated lattice fermions

Abstract

The problem of finding of the ferromagnetic and antiferromagnetic "symmetry broken" solutions of the correlated lattice fermion models beyond the mean-field approximation has been investigated. The calculation of the quasiparticle excitation spectra with damping for the single-and multi-orbital Hubbard model has been performed in the framework of the equation-of-motion method for two-time temperature Green's Functions within a nonperturbative approach. A unified scheme for the construction of Generalized Mean Fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation has been generalized in order to include the presence of the "source fields". The damping of quasiparticles, which reflects the interaction of the single-particle and collective degrees of freedom has been calculated. The "symmetry broken" dynamical solutions of the Hubbard model, which correspond to various types of itinerant antiferromagnetism has been discussed. This approach complements previous studies and clarifies the nature of the concepts of itinerant antiferromagnetism and "spin-aligning field" of correlated lattice fermions. * Physica A267 (1999) 131-152 †

Spectral Properties of the Generalized Spin-Fermion Models

“…The main advantage of the approach of paper [19] was the using of concept of "anomalous averages" (c.f. [25]) fixing the relevant (Neel) vacuum and providing a possibility to determine properly the generalized mean fields. The functional structure of required GF has the following matrix form…”

Quasiaverages, symmetry breaking and irreducible Green functions method

“…The question of symmetry breaking within the localized and band models of antiferromagnets was studied by the author of this work in [22,32,37,51]. It has been found therein that the concept of spontaneous symmetry breaking in the band model of magnetism is much more complicated than in the localized model.…”

“…With this definition, one introduces the so-called anomalous (off-diagonal) Green functions which fix the relevant vacuum and select the proper symmetry broken solutions. The theory of itinerant antiferromagnetism [37] was formulated by using sophisticated arguments of irreducible Green functions method in complete analogy with our description of the Heisenberg antiferromagnet at finite temperatures [32]. For a two-sublattice antiferromagnet we used the matrix Green function of the form …”

“…It becomes clear that only a thorough experimental and theoretical investigation of quasiparticle many-body dynamics of the many-particle systems can provide an answer to the relevant microscopic picture [22]. In our works, we discussed the microscopic view of a dynamic behaviour of various interacting manybody systems on a lattice [22,[30][31][32][33][34][35][36][37][38][39][40]. A comprehensive description of transition and rare-earth metals and alloys and other materials (as well as efficient predictions of properties of new materials) is possible only in those cases, where there is an adequate quantum-statistical theory based on the information about the electron and crystalline structures.…”

“…The source of difficulties here lies not only in the complexity of calculations of certain dynamic properties (such as, the density of states, electrical conductivity, susceptibility, electron-phonon spectral function, the inelastic scattering cross section for slow neutrons), but also in the absence of a well-developed method for a consistent quantum-statistical analysis of a many-particle interaction in such systems. A self-consistent field approach was used in the papers [22,[30][31][32][33][34][35][36][37][38][39][40] for description of various dynamic characteristics of strongly correlated electronic systems. It allows one to consistently and quite compactly compute quasiparticle spectra for many-particle systems with strong interaction taking into account damping effects.…”