A local Hamiltonian is built from interactions with restricted support. In quantum-information terminology, a k-local Hamiltonian has terms acting on at most a fixed number of subsystems. Geometric locality adds that those subsystems are nearby in a specified spatial arrangement.
A nearest-neighbor spin chain satisfies both requirements. A sum of interactions between arbitrary distant pairs is two-local in the support-counting sense but need not be geometrically local. This distinction matters when estimating propagation, simulation cost and hardware connectivity. Locality constrains individual terms, not whether the evolved state stays unentangled: repeated local interactions can spread correlations across the system. The geometry, interaction range and strength assumptions must accompany a dynamical locality claim.
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