Comparison of three different self-interaction corrections for an exactly solvable model system

A systematic comparison of three approximate self-interaction corrections (SICs), Perdew-Zunger SIC, Lundin-Eriksson SIC and extended Fermi-Amaldi SIC, is performed for a model Hamiltonian whose exact many-body solution and exact local-density approximation (LDA) are known. For each of the three proposals we compare its implementation only for the potential, only for the energy, i.e., a post-LDA evaluation of the SIC energy), to none of them, i.e., a standard LDA calculation) and to both. Each of the resulting 10 permutations of methodologies is applied to 420 Hubbard chains differing in size, particle number and interaction strength. A statistical analysis of the resulting data set reveals trends and permits to assess the performance of each methodology. Overall, but not in each individual case, a post-LDA application of Perdew-Zunger SIC emerges as the recommended methodology.