Theory of condensed matter and new materials

Abstract

An attempt is made to analyze the present state of first-principles methods used in solid state theory to elucidate where these methods derive their strength and why they may be expected to gain even more predictive power in the near future. The latter will depend on the success of recently contemplated improvements. As regards the ground state properties of solids, there are two—in principle— rigorous ways of treating the associated N-electron problem. One is based on the Hohenberg-KohnSham (HKS) theory, which maps the electronic pair correlation onto a strictly local, energy-independent potential that occurs in the associated one-particle equations. The alternative approach, which will not be discussed in this paper, is connected with determining quasi-particle amplitudes from the Dyson equation, where the information on the electronic pair correlation is absorbed into a nonlocal energy-dependent self-energy operator. Distinctly different from HKS theory, which only applies to ground states, the quasi-particle scheme lends itself to describe excitations (e.g., interband transitions) just as well. We shall furthermore discuss a generalization of the HKS theory that explains why naive extensions of this approach to excited states have been relatively successful in a variety of cases.