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First principles approaches have been successful in solving many-bodyHamiltonians for real materials to an extent when correlations are weak ormoderate. As the electronic correlations become stronger often embeddingmethods based on first principles approaches are used to better treat thecorrelations by solving a suitably chosen many-body Hamiltonian with a higherlevel theory. Such combined methods are often referred to as second principlesapproaches. At such level of the theory the self energy, i.e. the functionalthat embodies the stronger electronic correlations, is either a function ofenergy or momentum or both. The success of such theories is commonly measuredby the quality of the self energy functional. However, self-consistency in theself-energy should, in principle, also change the real space chargedistribution in a correlated material and be able to modify the electroniceigenfunctions, which is often undermined in second principles approaches. Herewe study the impact of charge self-consistency within two example cases:TiSe$_{2}$, a three-dimensional charge-density-wave candidate material, andCrBr$_{3}$, a two-dimensional ferromagnet, and show how real space chargere-distribution due to correlation effects taken into account within a firstprinciples Green's function based many-body perturbative approach is key indriving qualitative changes to the final electronic structure of thesematerials.

First principles vs second principles: Role of charge self-consistency in strongly correlated systems