Overcoming the noncausality problem in nonlocal extensions of dynamical mean-field theory

In the last decade non-local extensions of the highly successful dynamical mean-field theory (DMFT) have become state of the art in order to access various phenomena that arise from nonlocal correlations. Though, it was realized that the success of these methods can be hampered by the emergence of noncausal features in the effective or observable quantities involved. We present a new approach of extending the local DMFT equations to nonlocal correlations, which preserves causality and has a physically intuitive interpretation. This approach has general implications for all related methods, and can be adapted with minimal effort for cluster, dual boson or fermion techniques. We benchmark the method for the exactly solvable dimer problem, which shows a significant improvement in the quality of the results compared to the standard approach.