Strongly Correlated Systems Theoretical Methods
The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic qu
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Density Functional Theory: A Personal View Robert O. Jones
Abstract A practical definition of “strongly correlated” systems covers those that cannot be described well by density functional (DF) theory. DF theory has become an indispensable part of computational condensed matter physics and chemistry, but its origins go back to the early years of quantum mechanics in the late 1920s, and this chapter is devoted to a historical view of its development. Thomas and Fermi recognized the electron density as a basic variable, and Dirac showed already in 1930 that the state of an atom is completely determined by its density; it is not necessary to specify the wave function. We follow the development of these ideas in the following decades to the single-particle equations of Kohn and Sham in 1965. Many details of the history are not well known, even to specialists in the field. The single application discussed is the Be2 , which was perhaps the first unexpected DF prediction on small molecules that proved to be correct.
1.1 Introduction Many seminars and publications on “strongly correlated” systems mention at the outset the widespread use of density functional (DF) theory in condensed matter physics and chemistry and point out the physical insight that often results. The second sentence, however, often lists the systems where DF results are disastrous (an insulator is found to conduct, almost anything to do with rare earth elements, etc.), emphasizing the importance of describing strongly correlated materials correctly
R.O. Jones () Institut f¨ur Festk¨orperforschung, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany German Research School for Simulation Sciences, RWTH Aachen University and FZ J¨ulich, 52425 J¨ulich, Germany e-mail: [email protected] A. Avella and F. Mancini (eds.), Strongly Correlated Systems, Springer Series in Solid-State Sciences 171, DOI 10.1007/978-3-642-21831-6 1, © Springer-Verlag Berlin Heidelberg 2012
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(see, e.g., the Foreword of this volume). At first sight, one might wonder about the relevance of an article on DF theory in a book devoted to the areas where it fails. Further reflection, however, suggests that we should have a feel for the areas where it does a good job, i.e., cases where physical insight can be obtained without recourse to the methods described in other articles in this volume. It is also important to know why approximations used in DF calculations should give sensible answers far from their regions of obvious validity. Yes, the DF approach should be understood by all who are interested in systems where it fails, and the editors have asked me to help you. The DF formalism shows that ground state properties of a system of electrons in an external field can be determined from a knowledge of the density distribution n.r/ alone; one does not need to know the much more complicated many-electron wave function. We shall see below that this remarkable result was proved by Dirac [1] already in 1930. We focus in this article on a property for which DF calculation
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