Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath

TL;DR

This paper introduces two fast algorithms based on the inclusion-exclusion principle to efficiently sum bosonic diagrams in quantum Monte Carlo methods, extending previous fermionic work and significantly reducing computational complexity.

Contribution

The paper develops novel algorithms that extend inclusion-exclusion techniques to bosonic systems in quantum Monte Carlo, reducing complexity from double factorial to exponential.

Findings

Algorithms significantly reduce computational complexity.

Numerical experiments confirm theoretical efficiency gains.

Extension of fermionic methods to bosonic systems.

Abstract

We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theoretical results and to compare the efficiency of the methods.