Towards combining dynamical mean-field theory with diagrammatic Monte Carlo

Dynamical mean-field theory (DMFT) has been successfully combined with Density Functional Theory and other weak coupling diagrammatic methods such as GW, Hartree-Fock, and second order perturbation theory. But all these methods are uncontrolled and their success is sensitive to the choices made in the approximations or the starting point. Here, we explore how DMFT can be turned into a numerically controlled method by systematically adding to the DMFT approximation the higher order Feynman diagrams order by order using the diagrammatic Monte Carlo method.

The intersection of DMFT and the weak coupling method needs to be subtracted carefully as an exact double counting term, which is here rigorously defined and identified. Since the building blocks of the diagrammatic theory are the DMFT Green's functions, the series is expected to converge faster than with a weak coupling starting point, as the local correlations are already accounted for exactly. The scheme is tested on the H₂ molecule in a Gaussian basis set, using second- and third-order diagrams added to DMFT, and iterating to charge self-consistency.