Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

TL;DR

This paper introduces a novel normalizing flow-based method with an annealing scheme to effectively address the sign problem in doped Hubbard model simulations, enabling more accurate and ergodic sampling at finite chemical potential.

Contribution

It extends normalizing flows to finite doping in the Hubbard model, improving ergodicity and accuracy over traditional methods.

Findings

Accurately reproduces exact diagonalization results.

Reduces statistical uncertainties by an order of magnitude.

Enables ergodic sampling at finite chemical potential.

Abstract

The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.