Implementation of Dyson equation to accelerate convergence in RS-LMTO-ASA code

Sammanfattning: First-principle calculations is a key ingredient for us to understand, improve and design new materials. Density functional theory (DFT) [1] has proven to be a very powerful tool and a number of different versions exist depending on the problem at hand. A crucial perspective brought by DFT, thanks to the Hohenberg-Kohn theorems, is that all the information needed is contained in the ground state electronic density and that the density that minimizes the energy functional is the true density. This shift the problem from solving a many-body Schrödinger equation to an easier problem of solving single-particle Kohn-Sham equations where each electron interacts with the electronic density. One can then solve the problem self-consistently, iterating until the global minimum is reached. The most expensive part computationally is the inversion of a large Hamiltonian, with the help of the Recursion Method [4]. The goal of the project was to skip this step in some of the iterations by solving the Dyson equation to get a new Green's function from the old one and the parameters used to construct the Hamiltonian. The implemented Dyson recursion algorithm, into the self-consistent process of the RS-LMTO-ASA code, indicates that we in some cases do improve convergence time of the studied systems, showing a great decrease of the number of regular Hamiltonian inversions, using linear mixing, needed to get to a low moment difference.