Integrating dynamical mean-field theory and diagrammatic Monte Carlo

Dynamical mean-field theory (DMFT) is one of the most widely used theoretical methods for electronic structure calculations, providing self-consistent solutions even in low-temperature regimes, which are exact in the limit of infinite dimension. The principal limitation of this method is that it neglects spatial fluctuations, which become important in finite dimensions. Diagrammatic Monte Carlo (diagMC), by contrast, provides results that are asymptotically exact for a convergent or resummable series, but are typically limited to high temperature as they depend on the analytic structure of the expansion. In this work, we present a framework for integrating these two methods so that the diagrammatic expansion is conducted around the DMFT solution. This results in a series expansion conducted only in terms that explicitly depend on nonlocal correlations, and which is asymptotically exact.