Study of influence of non-local interactions on the properties of the systems with strong electron correlations

Abstract: Systems with 3d-transition metals can be perfectly described by the lattice Hubbard model [1], which can be solved by the Dynamical Mean-Field Theory (DMFT) [2]. In that case we suggest, that the interactions between electrons are only on the site of the lattice. But, according to recent studies [3], it was found there are strongly correlated systems, in which interactions between sites cannot be neglected. In that case it is necessary to solve the Extended Hubbard model [3] to obtain more realistic description of the material. One can do it using the Extended Dynamical Mean-Field Theory (EDMFT) [4].
This research is devoted to development of numerical scheme to solve equations of EDMFT. The scheme is based on the exact diagonalization approach. On the one hand, we have developed a numerical complex for EDMFT as one of the main results of this work. Also we determined a minimal parameterization of the effective impurity model for different types of interactions, that can significantly save required computational resources. On the other hand, we considered influence of charge and magnetic non-local interactions on the properties of a model system; screening of local Coulomb parameter accounting the non-local charge interaction; constructed the phase diagrams for both a square, and a triangular model lattices; as a real synthesized system we considered a functionalized graphene as well.

[1] Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. — 276, № 1365, p. 238–257 (1963).
[2] Rev. Mod. Phys. 68, 1, p. 13-125 (1996). Rev. Mod. Phys. 78, 3, p. 865-951 (2006).
[3] Phys. Rev. B. 94, 214411 (2016). Phys. Rev. Lett. 110, 166401 (2013). Phys. Rev. B. 94, 224418 (2016). Phys. Rev. Lett. 111, 036601 (2013). Phys. Rev. B. 74, 212507 (2006).
[4] Phys. Rev. Lett. 70, 21, p.3339-3342 (1993). Phys. Rev. B. 59, 8, p.5341-5360 (1999). Phys. Rev. Lett. 84, 16, p.3678-3681 (2000). Phys. Rev. B. 63, 11, 115110 (2001). Nature 413, p.804-808 (2001). Phys. Rev. B. 61, 8, p.5184-5193 (2000). Phys. Rev. Lett. 77, 16, p.3391-3394 (1996). PRB 52, 14, pp. 10295-10302 (1995).