Entanglement area law

An entanglement area law bounds a region's entanglement entropy by its boundary size rather than its volume, in a specified family of states and with a stated short-distance convention. For a lattice region $A$, a typical form is $S(A)\le c|\partial A|$ with a constant independent of the region's linear size.

The physical intuition is that correlations contributing most strongly across the cut can be concentrated near its boundary. A generic highly entangled state need not satisfy this: independent Bell pairs joining many interior sites to the exterior can produce volume-scaling entropy. Tensor-network area-law bounds make the boundary counting explicit through the number of cut bonds. Area laws are therefore useful structural constraints, not automatic consequences of calling a state quantum or a Hamiltonian local.

If a bipartition cuts $n_{\partial }$ tensor-network bonds of dimension at most $\chi$, its Schmidt rank is at most ${\chi }^{n_{\partial }}$ and its entanglement entropy is at most $n_{\partial }\log \chi$.