FI Computational Methods and Data Science Journal Club
Flatiron Institute, 162 5th Avenue
Speaker: Domenico DiSante (CCQ)
Title: Deep Learning the Functional Renormalization Group Flow for Correlated Fermions
I will present 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. It will be shown 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. In addition, a Dynamic Mode Decomposition analysis confirms that a small number of modes are indeed sufficient to capture the fRG dynamics.
This talk will demonstrate 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.
Besides the specific application to correlated fermions, I will discuss a dimensionality reduction scheme that may be useful to any research field dealing with presumable very high-dimensional data.
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