Deep Learning the Functional Renormalization Group

Autor(en)

Domenico Di Sante, Matija Medvidović, Alessandro Toschi, Giorgio Sangiovanni, Cesare Franchini, Anirvan M. Sengupta, Andrew J. Millis

Abstrakt

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(en)

Computergestützte Materialphysik

Externe Organisation(en)

Università di Bologna, Flatiron Institute, Columbia University in the City of New York, Technische Universität Wien, Julius-Maximilians-Universität Würzburg, Rutgers University

Journal

Physical Review Letters

Band

129

Anzahl der Seiten

7

ISSN

0031-9007

DOI

https://doi.org/10.1103/PhysRevLett.129.136402

Publikationsdatum

09-2022

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 102019 Machine Learning

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/16aa9694-21b5-4522-9205-a3cf6955c00d