Deep Learning the Functional Renormalization Group

Author(s)
Domenico Di Sante, Matija Medvidović, Alessandro Toschi, Giorgio Sangiovanni, Cesare Franchini, Anirvan M. Sengupta, Andrew J. Millis
Abstract

We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional t-t′ Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a neural ordinary differential equation solver in a low-dimensional latent space efficiently learns the FRG dynamics that delineates the various magnetic and d-wave superconducting regimes of the Hubbard model. We further present a dynamic mode decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the FRG dynamics. Our Letter demonstrates the possibility of using artificial intelligence to extract compact representations of the four-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.

Organisation(s)
Computational Materials Physics
External organisation(s)
University of Bologna, Flatiron Institute, Columbia University in the City of New York, Technische Universität Wien, Julius-Maximilians-Universität Würzburg, Rutgers University
Journal
Physical Review Letters
Volume
129
No. of pages
7
ISSN
0031-9007
DOI
https://doi.org/10.1103/PhysRevLett.129.136402
Publication date
09-2022
Peer reviewed
Yes
Austrian Fields of Science 2012
103015 Condensed matter, 102019 Machine learning
ASJC Scopus subject areas
Physics and Astronomy(all)
Portal url
https://ucris.univie.ac.at/portal/en/publications/deep-learning-the-functional-renormalization-group(16aa9694-21b5-4522-9205-a3cf6955c00d).html