Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows
This work addresses a critical bottleneck for simulating doped correlated systems in condensed matter physics, offering a significant improvement over existing methods.
The authors tackled the sign problem in the doped Hubbard model by extending normalizing flows with an annealing scheme to enable ergodic sampling, achieving accurate results with a tenfold reduction in statistical uncertainties compared to hybrid Monte Carlo.
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.