DFT+DMFT versus DFT+U description of Mott insulators: DMFT restores spin and orbital symmetry and removes metastables states

In the last twenty years, the developpement of methods based on the coupling of Density Functional Theory in the Local Density Approximation and Hubbard-like terms has led to a successfull description of many strongly correlated systems. These methods include DFT+U which contains a static description of interaction and the combination of DFT with Dynamical Mean Field Theory (DFT+DMFT) which adds fluctutations to the description of interactions. We present implementations of DFT+U and DFT+DMFT in the same framework, and with the same approximations. We show, in agreement with previous results in the litterature, and even in the simple Hubbard I approximation to DMFT,that DFT+DMFT is able to describe Mott insulator without any breaking of spin and orbital symmetry. We show that this improvement simply remove the appearance of metastable states, and thus solve a practical and physical problem encountered in particular in the description of actinides oxydes in DFT+U calculations.