Toward Scalable Normalizing Flows for the Hubbard Model

TL;DR

This paper explores extending normalizing flows to larger lattices and lower temperatures in the Hubbard model, analyzing their scalability, stability, and efficiency for advanced condensed matter simulations.

Contribution

It introduces methods to improve the scalability and stability of normalizing flows for larger and more complex Hubbard model simulations.

Findings

Normalizing flows can learn the Hubbard model distribution.

Scaling behavior of stochastic flows is characterized.

Enhanced stability methods enable larger lattice simulations.

Abstract

Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. Additionally, we present the scaling behavior of stochastic normalizing flows and non-equilibrium Markov chain Monte Carlo methods for this fermionic system.