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arXiv · 2202.13268

Deep Learning the Functional Renormalization Group

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

We perform a data-driven dimensionality reduction of the scale-dependent 4-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 work demonstrates the possibility of using artificial intelligence to extract compact representations of the 4-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.

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BibTeXRIS

Domenico Di Sante, Matija Medvidović, Alessandro Toschi, Giorgio Sangiovanni, Cesare Franchini, Anirvan M. Sengupta, Andrew J. Millis. 2022-02-27. Deep Learning the Functional Renormalization Group. https://doi.org/10.1103/physrevlett.129.136402

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