Investigation of Self-Interaction Corrections for an Exactly Solvable Model System: Orbital Dependence and Electron...

Area of Science:

• Computational physics
• Quantum chemistry
• Condensed matter theory

Background:

• The self-interaction error in density functional theory (DFT) approximations like LDA can lead to delocalization errors.
• Self-Interaction Correction (SIC) methods aim to mitigate this error by accounting for the self-interaction of an electron with itself.

Purpose of the Study:

• To systematically investigate the performance of two approximate SICs (Perdew-Zunger SIC and Lundin-Eriksson SIC) against the local-density approximation (LDA).
• To analyze their behavior on one-dimensional Hubbard chains with varying parameters, focusing on ground-state properties and electron localization.

Main Methods:

• Application of Perdew-Zunger SIC, Lundin-Eriksson SIC, and LDA to one-dimensional Hubbard chains.
• Utilizing the optimized-effective potential (OEP) method, reformulated for the Hubbard model, to handle orbital-dependent SIC potentials.
• Calculation of ground-state energies, densities, energy gaps, and impurity densities.

Main Results:

• Comparison of LDA's delocalization tendency with the localization tendency induced by both SIC methods.
• Statistical analysis of results for weakly and strongly interacting systems.
• Assessment of the performance of SIC methods versus LDA for model Hamiltonians with known exact solutions.

Conclusions:

• Approximate SICs demonstrate a propensity to localize electrons, contrasting with LDA's delocalization.
• The study provides a quantitative assessment of SIC and LDA performance, informing future development of more accurate electronic structure methods.