Deep Learning the Functional Renormalization Group

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 -t0 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.

Automated summary

In this paper, a data-driven dimensionality reduction approach is applied to the functional renormalization group dynamics of the widely studied two-dimensional Hubbard model. By using a deep learning architecture based on a neural ordinary differential equation solver, the authors efficiently learn the various magnetic and d-wave superconducting regimes of the model. The results demonstrate the potential of using artificial intelligence to extract compact representations of vertex functions for correlated electrons, which is crucial for cutting-edge quantum field theoretical methods in solving many-electron problems.