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In a local gapped ground state, correlations and the entanglement that lower local interaction energies are concentrated within a finite correlation length. A degree of freedom deep inside a region uses most of its entanglement with nearby degrees of freedom that are also inside. Entanglement monogamy limits its simultaneous entanglement with the exterior, so only degrees of freedom within a correlation-length layer of the boundary can contribute extensively across the cut. Their number scales as the boundary area, suggesting the entanglement area lawThis is a physical argument rather than a proof from monogamy alone; locality and suitable ground-state assumptions are essential.

In a local gapped ground state, correlations and the entanglement needed to lower a local interaction energy are concentrated over a finite distance. Degrees of freedom deep inside a region use most of their entanglement with nearby degrees of freedom that are also inside; entanglement monogamy limits their simultaneous entanglement with the exterior. Only degrees of freedom within a correlation length of the boundary can contribute extensively across the cut, giving an entanglement area lawMonogamy supplies the physical mechanism, while locality and suitable ground-state assumptions are essential; monogamy alone is not a general mathematical proof of an area law.