English   español  
Por favor, use este identificador para citar o enlazar a este item: http://hdl.handle.net/10261/137516
logo share SHARE logo core CORE   Add this article to your Mendeley library MendeleyBASE

Visualizar otros formatos: MARC | Dublin Core | RDF | ORE | MODS | METS | DIDL
Exportar a otros formatos:

The Hubbard dimer: a density functional case study of a many-body problem

AutorCarrascal, Diego ; Ferrer, Jaime ; Smith, Justin; Burke, Kieron
Palabras claveHubbard model
Density functional theory
Strongly correlated electron systems
Fecha de publicación2015
EditorInstitute of Physics Publishing
CitaciónJournal of Physics: Condensed Matter 27: 393001 (2015)
ResumenThis review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
Versión del editorhttp://dx.doi.org/10.1088/0953-8984/27/39/393001
Identificadoresdoi: 10.1088/0953-8984/27/39/393001
e-issn: 1361-648X
issn: 0953-8984
Aparece en las colecciones: (CINN) Artículos
Ficheros en este ítem:
Fichero Descripción Tamaño Formato  
HubbardDimer.pdf1,24 MBAdobe PDFVista previa
Mostrar el registro completo

NOTA: Los ítems de Digital.CSIC están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario.