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

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+$\Sigma$ approach incorporates the above interactions by introducing into the general DMFT model an additional (generally momentum-dependent) self-energy $\Sigma$ 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+$\Sigma$ 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+$\Sigma$ approach is employed to calculate pseudogap states in electron- and hole-doped HTSC cuprates. Comparisons with angle-resolved photoemission spectroscopy (ARPES) results are presented.