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

TL;DR

This paper introduces a versatile 'bold-line' diagrammatic Monte Carlo framework that enhances the accuracy of quantum many-body calculations by incorporating analytical resummations, demonstrated on the Anderson model and dynamical mean field theory.

Contribution

It develops a general bold-line Monte Carlo method that uses partial resummation as a starting point, improving the treatment of strongly correlated systems.

Findings

Accurately solves the Anderson model using the non-crossing approximation as a starting point.

Demonstrates high accuracy in describing the Mott-insulating phase.

Validates the approach within single-site dynamical mean field theory.

Abstract

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.