Deep Learning the Functional Renormalization Group
Deep Learning the Functional Renormalization Group

    
    
                
    View PDF
            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.
    

    
    
  
      Submission history From: Domenico Di Sante Dr [view email]                  [v1]
        Sun, 27 Feb 2022 02:11:36 UTC (787 KB)
    [v2]
        Tue, 28 Mar 2023 09:32:55 UTC (1,104 KB)
