Exact double-counting in combining the Dynamical Mean Field Theory and the Density Functional Theory

We propose a continuum representation of the Dynamical Mean Field Theory, in which we were able to derive an exact overlap between the Dynamical Mean Field Theory and band structure methods, such as the Density Functional Theory. The implementation of this exact double-counting shows improved agreement between theory and experiment in several correlated solids, such as the transition metal oxides and lanthanides. Previously introduced nominal double-counting is in much better agreement with the exact double-counting than most widely used fully localized limit formula.