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  • Letter
  • Open Access

Simulating correlated electrons with symmetry-enforced normalizing flows

Dominic Schuh1,2,*, Janik Kreit1,2,†, Evan Berkowitz3,4,5,6, Lena Funcke1,2, Thomas Luu2,4, Kim A. Nicoli1,2,7, and Marcel Rodekamp8

  • *Contact author: schuh@hiskp.uni-bonn.de
  • †Contact author: jkreit@uni-bonn.de
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Phys. Rev. Research 8, L012071 – Published 25 March, 2026

DOI: https://doi.org/10.1103/4741-cvvs

Abstract

We present the first proof of principle that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model—a key framework for describing the electronic structure of graphene and related materials. State-of-the-art methods like hybrid Monte Carlo often suffer from ergodicity issues near the time-continuum limit, leading to biased estimates. Leveraging symmetry-aware architectures as well as independent and identically distributed sampling, our approach resolves these issues and achieves significant speedups over traditional methods.

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Phys. Rev. Research 8, L012071– Published 25 March, 2026
  • Received 22 July 2025
  • Accepted 28 January 2026
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