Transformer Foundation Model for Quantum Ground States

Foundation models have reshaped AI by learning general-purpose representations from broad data. We bring this paradigm to many-body physics with a foundation wavefunction model that learns ground states directly. Our approach is a minimal-bias Transformer neural quantum state (NQS) that ingests only occupational (Fock) tokens and a single Hamiltonian token $\boldsymbol\lambda$ (e.g., $(t,V,N)$), with no hand-crafted features or symmetry encodings. Instead of minimizing energy, we supervise the network to maximize fidelity with exact-diagonalization (ED) wavefunctions, aligning amplitudes and phases and learning a smooth map $\boldsymbol\lambda\!\mapsto\!\Psi_\theta(\boldsymbol\lambda)$. On the 2D square-lattice $t$–$V$ model without sampling, we train up to 16 sites, reaching $>99.99\%$ overlap on training points and $>99.6\%$ on held-out parameters. We match ED energies within $1.5\%$ relative accuracy, and characterize ground state versus excited state learning. Our model's minimality, expressivity, and generality pavies the way for a more direct and unified approach to NQS.