Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation

We present a general framework for performing "bold-line" diagrammatic Monte Carlo calculations based on using an analytical partial resummation as a starting point for stochastically summing all diagrams. As an example we solve the one orbital Anderson model using the non-crossing approximation as a starting point. We assess the accuracy of the method by using it to solve the equations of single-site dynamical mean field theory. We establish the validity of the starting approximations and show that the bold method provides a very accurate treatment of the Mott-insulating phase.