Finite-size scaling of neural ansatz performance in solid-state simulations

Characterize how the performance—including accuracy, convergence behavior, and the required number of variational parameters—of neural-network wavefunction ansatzes for interacting electrons changes as the system size increases in periodic solid-state simulations, thereby quantifying finite-size effects.

Background

Finite-size effects are crucial in numerical simulations of solids due to periodic boundary conditions and supercell approximations. The paper introduces a self-attention-based neural ansatz and later reports an empirical parameter scaling N_par ∝ N^2.1 for moiré systems, suggesting favorable scaling compared to some tensor-network approaches.

The open question explicitly posed in the Introduction asks for a general understanding of how performance evolves with system size, beyond specific empirical observations, to guide reliable large-scale applications.