Accurate Self-Attention Wavefunctions at Large Scale
arXiv:2607.08616
The authors apply self‑attention neural network variational wavefunctions to the two‑dimensional homogeneous electron gas with up to 169 particles, achieving energies lower than state‑of‑the‑art diffusion Monte Carlo and accurately reproducing collective excitations, indicating convergence to the thermodynamic limit.
Abstract
Self-attention neural networks provide powerful variational wavefunctions that surpass the expressivity of traditional variational ansatze. This expressivity, however, comes with increased computational complexity, raising a pressing question about scalability -- can such wavefunctions retain their accuracy at large system sizes? We apply self-attention wavefunctions to the two-dimensional homogeneous electron gas for up to N=169 particles, obtaining energies systematically lower than state-of-the-art DMC. Direct access to the ground state wavefunction further lets us recover the full collective-mode dispersion of the liquid phase, from the small-q plasmon branch to a roton-like minimum near q=2k_F. Observables at N=91 and N=169 are in near-perfect agreement, indicating convergence to the thermodynamic limit.