Electronic structure calculations of strongly correlated electron systems by the dynamical mean-field method

In recent years understanding of the physics of strongly correlated materials has undergone tremendous increase. This is in part due to the advances in the theoretical treatments of correlations, such as the development of dynamical mean-field theory DMFT .1 This approach offers a minimal description of the electronic structure of correlated materials, treating both the Hubbard and the quasiparticle bands on the same footing. It becomes exact in the limit of infinite lattice coordination introduced in the pioneering work of Metzner and Vollhardt.2 The great allure of DMFT is the flexibility of the method and its adaptability to different systems as well as the simple conceptual picture it allows us to form of the dynamics of the system. The mean-field nature of the method and the fact that the solution maps onto an impurity model, many of which have been thoroughly studied in the past, means that a great body of previous work can be brought to bear on the solution of models of correlated lattice electrons. This is exemplified by the great many numerical methods that can be employed to solve the DMFT equations. DMFT has been very successful in understanding the mechanism of the Mott transition in model Hamiltonians. We now understand that the various concentration-induced phase transitions can be viewed as bifurcation of a single functional of the Weiss field. The phase diagram of the one-band Hubbard model, demonstrating that there is a first-order Mott transition at finite temperatures, is fully established.1 Furthermore Landau-like analysis demonstrates that all the qualitative features are quite generic at high temperatures.3 However, the low-temperature ordered phases and the quantitative aspects of the spectra of specific materials clearly require realistic treatment. This triggered realistic development of DMFT in the last decade which has now reached the stage that we can start tackling real materials from an almost ab initio approach,4,5 something which in the past has been exclusively in the domain of density functional theories. We are now starting to see the merger of DMFT and such ab initio techniques and consequently the opportunities for doing real electronic structure calculations for strongly correlated materials which so far were not within the reach of traditional density functional theories. Density functional theory6 DFT is the canonical example of the ab initio approach, very successful in predicting ground-state properties of many systems which are less correlated, for example the elemental metals and semiconductors. However, it fails in more correlated materials. It is unable to predict that any system is a Mott insulator in the absence of magnetic order. It is also not able to describe correctly a strongly correlated metallic state. As a matter of principle DFT is a theory of the ground state. Its Kohn-Sham spectra cannot be rigorously identified with the excitation spectra of the system. In weakly correlated substances the Kohn-Sham spectra is a good approximation to start a perturbative treatment of the one-electron spectra using the GW method.7 However, this approach breaks down in strongly correlated situations, because it is unable to produce Hubbard bands. In orbitally ordered situations the local density approximation LDA +U method8 produces the Hubbard bands; however, this method fails to produce quasiparticle bands and hence it is unable to describe strongly correlated metals. Furthermore, once long-range order is lost the LDA+U method reduces to the LDA and hence it becomes inappropriate even for Mott insulators. Dynamical mean-field theory is the simplest theory that is able to describe on the same footing total energies and the spectra of correlated electrons even when it contains both quasiparticle and Hubbard bands. Combined with the LDA, one then has a theory which reduces to a successful method LDA in the weak-correlation limit. In the static limit, one can show9 that LDA+U can be viewed as a static limit of the LDA+DMFT used in conjunction with the Hartree-Fock approximation. Therefore the LDA+U is equivalent to the LDA+DMFT+further approximations which are only justified in static ordered situations. Up to now, the realistic LDA PHYSICAL REVIEW B 73, 03512