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Learning latent variable evolution for the functional renormalization group
Matija Medvidović · Alessandro Toschi · Giorgio Sangiovanni · Cesare Franchini · Andy Millis · Anirvan Sengupta · Domenico Di Sante

We perform a data-driven dimensionality reduction of the 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 show that a deep learning architecture based on a Neural Ordinary Differential Equations efficiently learns the evolution of low-dimensional latent variables in all relevant magnetic and d-wave superconducting regimes of the Hubbard model. Ultimately, our work uses an encoder-decoder architecture to extract compact representations of the 4-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge methods for tackling the many-electron problem.

Author Information

Matija Medvidović (Columbia University)
Alessandro Toschi (TU Wien)
Giorgio Sangiovanni (University of Wuerzburg)
Cesare Franchini (University of Bologna)
Andy Millis (Flatiron Institute)
Anirvan Sengupta (Flatiron Institute)
Domenico Di Sante (Flatiron Institute (CCQ Affiliate))

I am an Assistant Professor at the University of Bologna and a Marie Curie Research Fellow at the Center for Computational Quantum Physics of the Flatiron Institute in New York. I earned a B.S. in physics at the University of L’Aquila in 2011 and a Ph.D. in physics in 2015. I subsequently was a postdoctoral fellow and young group leader at the Physics Department of the University of Würzburg. My research is focused on the numerical quantum simulations of the electronic properties of non-interacting and interacting material systems, with emphasis on topology and spin-orbit driven phenomena. I am the principal investigator of an individual Marie Curie fellowship which aims at using machine learning applications in condensed matter problems.

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