Simulating the Hubbard Model with Equivariant Normalizing Flows
This work addresses ergodicity problems in numerical simulations of the Hubbard model for materials science, but it is incremental as it applies an existing method to a new domain.
The authors tackled the problem of ergodicity issues in simulating the Hubbard model, a model for electronic structure in materials like graphene, by using normalizing flows to learn the Boltzmann distribution, resulting in effective mitigation of biases in physical observables through i.i.d. sampling.
Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations. In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues.