Generalized dynamical mean-field theory in the physics of strongly correlated systems

Abstract

This review discusses the generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems to include additional interactions necessary for the correct description of physical effects in such systems. Specifically, the additional interactions include: (1) the interaction of electrons with antiferromagnetic (or charge) order-parameter fluctuations in high-temperature superconductors leading to the formation of a pseudogap state; (2) scattering on static disorder and its role in the general picture of the Anderson-Hubbard metal-insulator transition, and (3) electron-phonon interaction and the features of electronic spectra in strongly correlated systems. The proposed DMFT+ approach incorporates the above interactions by introducing into the general DMFT model an additional (generally momentum-dependent) self-energy which is calculated in a self-consistent way without violating the general structure of the DMFT iteration cycle. The paper formulates a general calculational scheme for both one-particle (spectral functions and densities of states) and two-particle (optical conductivity) properties. The problem of pseudogap formation is examined, including Fermi arc formation and partial destruction of the Fermi surface, as are the metal-insulator transition in the disordered Anderson-Hubbard model, and the general picture of kink formation in the electronic spectra of strongly correlated systems. A generalization of the DMFT+ approach to realistic materials with strong electron-electron correlations is presented based on the LDA+DMFT method. The general model of the LDA+DMFT method is reviewed, as are some of its applications to real systems. The generalized LDA+DMFT+ approach is employed to calculate pseudogap states in electron- and hole-doped HTSC cuprates. Comparisons with angle-resolved photoemission spectroscopy (ARPES) results are presented.