Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems

TL;DR

This paper presents a novel Diagrammatic Monte Carlo method that combines Feynman and angular momentum diagrams to analyze quantum many-particle systems with non-Abelian angular momentum algebra, applicable across various coupling regimes.

Contribution

The paper introduces a general DiagMC approach that merges Feynman and angular momentum diagrams, enabling error-free analysis of quantum systems with complex angular momentum interactions.

Findings

Successfully applied to the angulon model across all coupling strengths

Provides access to impurity Green functions without systematic errors

Applicable to a wide range of quantum many-particle systems

Abstract

We introduce a Diagrammatic Monte Carlo (DiagMC) approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model, however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.