Global sampling of Feynman's diagrams through normalizing flow

Author(s)
Luca Leoni, Cesare Franchini
Abstract

Normalizing flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in the diagrammatic Monte Carlo (DMC) method, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables one to construct a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC method is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables' statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in the DMC method.

Organisation(s)
Computational Materials Physics
External organisation(s)
University of Bologna
Journal
Physical Review Research
Volume
6
No. of pages
8
ISSN
2643-1564
DOI
https://doi.org/10.48550/arXiv.2402.00736
Publication date
07-2024
Peer reviewed
Yes
Austrian Fields of Science 2012
103015 Condensed matter, 102019 Machine learning, 103043 Computational physics
ASJC Scopus subject areas
General Physics and Astronomy
Portal url
https://ucrisportal.univie.ac.at/en/publications/034957c4-bb5c-4979-8b5b-febdbb69957c