Accurately simulating frustrated quantum spin models of thousands of sites using Neural-Network Quantum States

Neural-Network Quantum States (NQS) provide a powerful variational framework to represent quantum many-body wave functions. In this work, we introduce a modification of the Vision Transformer wave function to demonstrate that NQS can be trained from scratch to accurately capture the ground states of frustrated two-dimensional models on large system sizes, comprising thousands of spins. This unprecedented system size brings NQS-based simulations into the regime where thermodynamic-limit physics can be reliably extracted. Our results yield ground-state energies and correlation functions that compete with the most advanced numerical techniques based on tensor networks that operate directly in the thermodynamic limit.