By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional ab initio LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported. 71.15.Mb, 71.10.Pm, 71.10.Fd, 71.27.+a Density-functional theory (DFT) [1] is the basis of almost all of todays electronic-structure theory, and much of materials science and quantum chemistry. Many-body effects enter DFT via the exchange-correlation (xc) functional, which is commonly approximated by the localdensity approximation (LDA) [1]. The essence of the LDA is to locally approximate the xc energy of the inhomogeneous system under study by that of the homogeneous electron gas. This electron gas plays the role of a reference system, whose correlations are transfered by the LDA into the DFT description of the inhomogeneous system. The most popular improvement upon the LDA are generalized gradient approximations [2], whose basic philosophy is to abandon the requirement of homogeneity of the reference system. This system, however, is normally still the interacting electron gas [2].In the present paper we propose to explore a different paradigm for the construction of novel density functionals: instead of sticking to the electron gas as a reference system, and abandoning homogeneity, it may sometimes be advantageous to do the reverse: stick to homogeneity (and thus to the LDA) but abandon the electron gas as a reference system. The new reference system is chosen such that it accounts for the correlations present in the inhomogeneous system under study.The only requirement for the reference system is that in the absence of any spatially varying external potential its xc energy must be known exactly or to a high degree of numerical precision. Besides the electron gas (or Jellium model) there are many other physically interesting model systems that satisfy this criterium. Most notably among these is a large class of low-dimensional models which can be solved exactly by Bethe Ansatz (BA) techniques or bosonisation (in one dimension, e.g., the repulsive and the attractive Hubbard model, the hard-core Fermi and Bose gases, the Heisenberg, the supersymmetric t-J, and the Tomonaga-Luttinger model [3,4]). The solutions to these models in the homogeneous case can be used instead of the electron gas to construct LDA functionals that can then be applied to study these models also in inhomogeneous situations. The main advantage offered by a DFT treatment of such models is the gain in simplicity that arises from mapping the inhomogeneous interacting many-body system onto a noninteracting auxiliary system, which is diagonalized much more easily...

We show that the Auger Air Shower Array has the potential to detect neutrinos of energies in the 10 19 eV range through horizontal air showers. Assuming some simple conservative trigger requirements we obtain the acceptance for horizontal air showers as induced by high energy neutrinos by two alternative methods and we then give the expected event rates for a variety of neutrino fluxes as predicted in different models which are used for reference.PACS numbers: 95.85. Ry, 96.40.Tv, 96.40.Pq, 98.70.Sa 1

This paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of São Paulo at São Carlos, Brazil, and at the VIII'th Summer School on Electronic Structure of the Brazilian Physical Society. It is an attempt to introduce density-functional theory (DFT) in a language accessible for students entering the field or researchers from other fields. It is not meant to be a scholarly review of DFT, but rather an informal guide to its conceptual basis and some recent developments and advances. The Hohenberg-Kohn theorem and the Kohn-Sham equations are discussed in some detail. Approximate density functionals, selected aspects of applications of DFT, and a variety of extensions of standard DFT are also discussed, albeit in less detail. Throughout it is attempted to provide a balanced treatment of aspects that are relevant for chemistry and aspects relevant for physics, but with a strong bias towards conceptual foundations. The paper is intended to be read before (or in parallel with) one of the many excellent more technical reviews available in the literature.Keywords: Density-functional theory; Electronic-structure theory; Electron correlation; Many-body theory; Local-density approximation I. PREFACEThis paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of São Paulo at São Carlos, Brazil, and at the VIII'th Summer School on Electronic Structure of the Brazilian Physical Society [1]. The main text is a description of density-functional theory (DFT) at a level that should be accessible for students entering the field or researchers from other fields. A large number of footnotes provides additional comments and explanations, often at a slightly higher level than the main text. A reader not familiar with DFT is advised to skip most of the footnotes, but a reader familiar with it may find some of them useful.The paper is not meant to be a scholarly review of DFT, but rather an informal guide to its conceptual basis and some recent developments and advances. The Hohenberg-Kohn theorem and the Kohn-Sham equations are discussed in some detail. Approximate density functionals, selected aspects of applications of DFT, and a variety of extensions of standard DFT are also discussed, albeit in less detail. Throughout it is attempted to provide a balanced treatment of aspects that are relevant for chemistry and aspects relevant for physics, but with a strong bias towards conceptual foundations. The text is intended to be read before (or in parallel with) one of the many excellent more technical reviews available in the literature. The author apologizes to all researchers whose work has not received proper consideration. The limits of the author's knowledge, as well as the limits of the available space and the nature of the intended audience, have from the outset prohibited any attempt at comprehensiveness. II. WHAT IS DENSITY-FUNCTIONAL THEORY?Density-functional theory is one of the most popular and s...

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We study the Mott insulating phase of the one-dimensional Hubbard model using a local-density approximation (LDA) that is based on the Bethe Ansatz (BA). Unlike conventional functionals the BA-LDA has an explicit derivative discontinuity. We demonstrate that as a consequence of this discontinuity the BA-LDA yields the correct Mott gap, independently of the strength of the correlations. A convenient analytical formula for the Mott gap in the thermodynamic limit is also derived. We find that in one-dimensional quantum systems the contribution of the discontinuity to the full gap is more important than that of the band-structure gap, and discuss some consequences this finding has for electronic-structure calculations. 71.15.Mb, 71.10.Pm, 71.10.Fd The intricacies of the correlation-induced metalinsulator transition ('Mott transition') have fascinated and challenged physicists for many years, and a multitude of methods has been brought to bear on the problem [1]. Here we study the Mott insulator from the point of view of density-functional theory (DFT), a method whose full potential for exploring the Mott phenomenon has not been widely recognized. It may be particularly timely to study the prospects for a DFT treatment of the Mott insulating phase because this is one of the two main phases of the one-dimensional Hubbard model (1DHM), the paradigmatic model for low-dimensional quantum systems. The recent interest in nanotechnology has brought quasi one-dimensional systems, such as quantum wires and carbon nanotubes, into the focus of current research in many-body physics and materials science. DFT, on the other hand, is the de facto standard method for the calculation of the electronic structure of materials, but its applicability to the very peculiar phases typical of low-dimensional quantum systems has not been systematically investigated. Here we report on the application of a very recently developed density functional [2] to the Mott insulating phase of the 1DHM.DFT is often applied in a single-particle mode, in which the eigenvalues of the Kohn-Sham (KS) equation are interpreted as a mean-field approximation to the quasiparticle energies. It is well known that this approximation breaks down for systems with strong correlations, of which the Mott insulator is an example. On the other hand, as long as one restricts oneself to working with the particle density, the total ground-state energy, and quantities derivable from these, DFT is a rigorous manybody theory, whose predictive power is only limited by the quality of available approximations for the exchangecorrelation (xc) functional. It is in this many-body mode that we employ DFT here.The choice of the appropriate approximation for the xc functional depends on the system under study. Here we investigate the 1DHM, since this model represents a particularly clear case of a Mott transition, free of unessential complications: for nonzero interaction strength (U > 0) the 1DHM is a Mott insulator at half filling, whereas it is a Luttinger liquid (i.e., a one-dimens...

It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state densities are constructed. These findings imply that the zero-temperature exchangecorrelation energy is not always a differentiable functional of the spin density. As a consequence, various types of applications of SDFT must be critically reexamined. DOI: 10.1103/PhysRevLett.86.5546 PACS numbers: 71.15.Mb, 31.15.Ew, 75.10.Lp The Hohenberg-Kohn (HK) theorem [1], which guarantees that the ground-state single-particle density uniquely determines all observables of a many-body system, is one of the most remarkable theorems of quantum mechanics. It is also at the heart of density-functional theory (DFT), one of the most popular many-body methods [2,3]. In the case of the original formulation of DFT, in which the basic variable is the particle density n͑r͒, the HK theorem can be cast in the form of two logically independent one-to-one maps [2]. Quantum mechanics guarantees that, for a given interaction and particle number, the potential in which the particles move determines the ground-state many-body wave function (via solution of Schrödinger's equation), which in turn determines the ground-state density (by simple integration). The essence of the original HK theorem is that both of these maps are invertible: the ground-state density n͑r͒ uniquely determines the groundstate wave function C͑r 1 , . . . , r N ͒, which in turn determines, up to an additive constant, the potential [1-4],These abstract maps have found extremely important practical applications in the form of the Kohn-Sham (KS) formulation of DFT [5], which is used for almost all band-structure calculations in solid-state physics, and a rapidly increasing number of electronic-structure calculations in quantum chemistry. Many of these applications, however, do not employ the original formulation of DFT, but spin-density-functional theory (SDFT) [6], in which the fundamental variables are the spin-resolved particle densities n s ͑r͒. In SDFT the map from spin densities to wave functions is easily established, but that from wave functions to potentials could not, in spite of considerable effort [2,6,7] be proven and remains an, albeit popular, conjecture. In the early days of SDFT, von Barth and Hedin [6] already pointed out that the uniqueness of the spin-dependent potentials is not guaranteed, and explicitly constructed two potentials which, when used in a one-body Hamiltonian, have common eigenstates. The question of whether a similar construction is possible in the many-body case, however, remained open, and even in the one-body case it was objected that these common eigenstates were not necessarily common ground states [2,7].In this Letter, we settle these questions by first deriving a general equation [Eq. (2), below] whose solutions are the nonunique pieces of the potentials. This equation has two types of solutions, ...

We derive and analyze the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). The results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics. DOI: 10.1103/PhysRevLett.87.206403 PACS numbers: 71.15.Mb, 72.25. -b, 73.40. -c, 75.40.Gb The dynamics of the spin degrees of freedom is responsible for such diverse phenomena as spin wave excitations, Bloch wall motion, spin-polarized currents, spin injection, and spin filtering; concepts and phenomena which are important, e.g., in the growing field of spintronics [1]. The calculation of spin dynamics within density-functional theory (DFT) has consequently received much attention [2]. The most popular DFT method for a first-principles treatment of the spin degrees of freedom is spin-densityfunctional theory (SDFT, see Refs. [3,4] for reviews.) SDFT has led to versatile and powerful schemes for the calculation of, e.g., total energies, spin densities, and spin-resolved single-particle band structures, but its traditional (i.e., ground state) formulation is applicable only to static situations. This situation has changed with the advent of time-dependent DFT (TD-DFT) [5], which has brought dynamical phenomena within reach of DFT.In this Letter, we first derive the equation of motion for the spin magnetization from TD-SDFT, including exchange-correlation (xc) effects. We then show how this equation can be used to obtain information on the manybody spin current. Although one might think that a calculation of spin currents would require the more complex formalism of time-dependent current-density-functional theory (CDFT), we find that this is not entirely true: as a consequence of the continuity equation TD-SDFT suffices to calculate the spin currents in several cases of great practical interest.Numerical applications of TD-SDFT, as of any other DFT, require knowledge of the xc potentials, which contain all many-body effects beyond the Hartree approximation. In traditional DFT many exact properties of these xc potentials are known, and greatly aid the construction of good approximations [3,4], but the same is not true in the time-dependent case, where properties of the xc potentials are just beginning to be explored [6]. As a by-product, our analysis reveals a previously unknown exact property of the xc potentials of TD-SDFT, which strongly constrains suitable approximations.In TD-SDFT the fundamental variables are the timedependent particle density,and the time-dependent magnetization (or spin) densitywhere C C͑r 1 , . . . , r N , t͒ is the many-body wave function (spin ...

Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables ͑the current density and the superconducting order parameter, respectively͒ are included in the density-functional formalism. Here we show that the corresponding conjugate potentials ͑vector and pair potentials, respectively͒ are not uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences. DOI: 10.1103/PhysRevB.65.113106 PACS number͑s͒: 71.15.Mb, 31.15.Ew, 75.20.Ϫg, 74.25.Jb Today, density-functional theory 1 ͑DFT͒ is an indispensable tool for the investigation of the electronic structure of matter in atomic, molecular, or extended systems. The theory rests on the celebrated Hohenberg-Kohn ͑HK͒ theorem, 2 which guarantees that the (v-representable͒ ground-state density n(r) uniquely determines the ground-state manybody wave function 0 (r 1 , . . . ,r N ). This theorem on its own is a very powerful result, but in the original formulation 2,3 of DFT one can prove even more: the external potential v(r) ͑e.g., the nuclear charge distribution in a molecule or a solid͒, too, is a functional of the density, and is unique up to an additive constant. Since this external potential in turn determines all eigenstates of the many-body Hamiltonian, this implies that all observables ͑and not only ground state ones͒ are functionals of the ground-state density.Following original ideas of von Barth and Hedin, 4 it has recently been shown by Eschrig and Pickett 5 and by the present authors 6 that in spin-DFT ͑SDFT͒ the situation is not that simple: while the wave function is still uniquely determined by the spin densities n ↑ (r) and n ↓ (r), the external potentials v ↑ (r) and v ↓ (r) ͓or v(r) and B(r)͔ are not. This implies that SDFT functionals are not always differentiable, and has far-reaching consequences for the construction of better exchange-correlation ͑XC͒ functionals, and for applications to systems such as half-metallic ferromagnets. 5,6 SDFT is not the only instance at which the original HK theorem has been generalized. In the present work we extend the analysis of Ref. 6 to two other generalizations of DFT, namely, current-DFT 7,8 ͑CDFT͒ and DFT for superconductors. [9][10][11][12] The discovery of nonuniqueness in these generalized DFTs deepens our understanding of the respective XC functionals and flags a warning signal to alltoo-immediate generalizations of the original HK theorem to more complex situations.The basic physics of nonuniqueness is simple. When a sufficiently small change in one of the external fields does not change the corresponding density distribution, the associated susceptibility vanishes. The search for, and the interpretation of, nonuniqueness in DFT is thus guided by investigations of the circumstances under which some response function becomes zero.We first consider current-carrying systems. The appropriat...