Magnetic states and metal—insulator in strongly correlated systems (scientific summary)

Various slave particle approaches to the consideration of electron correlations in many-electron models, in particular, in application to layered copper oxide systems, have been analyzed. The magnetic phase diagrams of the ground state have been considered within the $t-t'$ Hubbard and $\mathrm{s}-\mathrm{d}$ exchange models for the square and cubic lattices depending on the degree of band filling and the interaction parameter with allowance for collinear ferromagnetic, antiferromagnetic, and incommensurate (helical) magnetic phases, as well as magnetic phase separation. The generalized Hartree–Fock and slave boson approaches including correlations have been used. The latter approach makes it possible to correctly include the contribution of doubly occupied sites to the energy and to adequately describe the paramagnetic phase. A criterion of a metal—insulator transition has been obtained by numerical calculations and the analytical expansion in the transfer integral between next-nearest neighbors $t'$ and in the direct antiferromagnetic gap $\Delta$. The order of the transition in the square lattice changes from the second to the first with increasing $t'$ at a small value of $t'\sim 0.05t$, which is due to the presence of a van Hove singularity near the band center. For the simple and body-centered cubic lattices, the transition from the antiferromagnetic insulator state occurs to an antiferromagnetic metal phase, is a second-order transition, and is followed by a transition to a paramagnetic metal. The inclusion of the intersite Heisenberg interaction changes these results and the transition can become a first-order transition.