Self-interaction corrections in density functional theory: investigation in models of many-body systems

Author(s)

Daniel Vieira

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2010-02-26

Examining board members

Klaus Werner Capelle; Maria Carolina de Oliveira Aguiar; Valter Luiz Libero; Eduardo Miranda; Thereza Cristina de Lacerda Paiva

• Advisor: Klaus Werner Capelle

Abstract

In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge. (AU)