Tackling critical slowing down using global correction steps with equivariant flows: the case of the Schwinger model

We propose a new method for simulating lattice gauge theories in the presence of fermions. The method combines flow-based generative models for local gauge field updates and hierarchical updates of the factorized fermion determinant. The flow-based generative models are restricted to proposing updates to gauge-fields within subdomains, thus keeping training times moderate while increasing the global volume. We apply our method performs to the 2-dimensional (2D) Schwinger model with $N_f=2$ Wilson Dirac fermions and show that no critical slowing down is observed in the sampling of topological sectors up to $\beta=8.45$. Furthermore, we show that fluctuations can be suppressed exponentially with the distance between active subdomains, allowing us to achieve acceptance rates of up to $99\%$ for the outer-most accept/reject step on lattices volumes of up to $V=128\times128$.