Local entropies across the Mott transition in an exactly solvable model

Spatial entanglement is a natural probe of delocalisation across metal-insulator transitions, but little is known of its behaviour in two or three dimensions near interaction-driven Mott transitions. We address this problem for the exactly solvable Hatsugai-Kohmoto model, whose Mott transition occurs at zero temperature between classically mixed states. We find that both its single-site entropy and its classical entropy density exhibit kinks at the Mott transition, only in one and two dimensions. Although the variation in entropy density across the transition dominates in the thermodynamic limit, the single-site entropy increases even as the degree of classical mixing is decreased. This suggests that the Hatsugai-Kohmoto model maintains quantum-coherent delocalisation even in the presence of classical mixing.