Simulating correlated electrons with symmetry-enforced normalizing flows

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.