Transformer wave function for quantum long-range models

We employ a neural-network architecture based on the vision transformer (ViT) architecture to find the ground states of quantum long-range models, specifically the transverse-field Ising model for spin-1/2 chains across different interaction regimes. Harnessing the transformer's capacity to capture long-range correlations, we compute the full phase diagram and critical properties of the model in both the ferromagnetic and antiferromagnetic cases. Our findings show that the ViT maintains high accuracy across the full phase diagram. We compare these results with previous numerical studies in the literature and, in particular, show that the ViT has a superior performance than a restricted-Boltzmann-machine-like ansatz.