Inclusion-Exclusion Principle for Many-Body Diagrammatics

TL;DR

This paper introduces a fast, scalable algorithm based on the inclusion-exclusion principle for summing diagrammatic expansions in fermionic quantum impurity models, significantly improving computational efficiency.

Contribution

The authors develop a novel algorithm that reduces the scaling of diagram summation from factorial to exponential, enabling more efficient Monte Carlo simulations.

Findings

Algorithm achieves two orders of magnitude speedup over previous methods.

Scales better asymptotically for large diagram classes.

Demonstrated effectiveness on a concrete physical model.

Abstract

Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually. We present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle to reduce the scaling from factorial to exponential. We analyze the growth rate and compare with related algorithms for expansions in the many-body interaction. An implementation demonstrates that for a simulation of a concrete physical model at reasonable parameters and accuracy, our algorithm not only scales better asymptotically, but also provides performance gains of approximately two orders of magnitude in practice over the previous state-of-the-art.