Simulating Correlated Electrons with Symmetry-Enforced Normalizing Flows
This work addresses a key problem in computational physics for simulating correlated electrons in materials, though it appears incremental as it builds on normalizing flows with symmetry enhancements.
The researchers tackled the challenge of accurately simulating the fermionic Hubbard model's Boltzmann distribution, which describes electronic structures in materials like graphene, by using symmetry-enforced normalizing flows to overcome ergodicity issues in existing methods and achieve significant speed-ups.
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 speed-ups over traditional methods.