The two-site Hubbard model (half-filling, one electron per site) captures the essence of the Mott transition. H = −t(c†↑σc↑σ + h.c.) + U(n↑₁n↓₁ + n↑₂n↓₂). As U/t increases from 0 to ∞, the ground state evolves from a delocalized metallic state to a localized Mott insulator. The exact 4-state solution reveals the charge gap Δ = U − √(U² + 16t²) + ... opening at U_c/t ≈ 3.