Self-consistent ladder dynamical vertex approximation

We present and implement a self-consistent D$\Gamma$A approach for multi-orbital models ab initio materials calculations. It is applied to the one-band Hubbard model at various interaction strengths with without doping, two-band two largely different bandwidths, SrVO$_3$. The self-energy feedback reduces critical temperatures compared dynamical mean-field theory, even zero temperature in two-dimensions. Compared one-shot, non-self-consistent calculation non-local correlations are significantly reduced when they strong. In case weak moderate as SrVO$_3$, one-shot calculations sufficient.