# Area law of entanglement entropy

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It is believed that the ground state entanglement entropy for a local gapped Hamiltonian satisfies an area law. That is, if we divide such a system in two parts A and B, then $S(\rho_A)=-Tr\left[\rho_A\log(\rho_A)\right]$ is proportional to the area of the boundary separating A and B, where $\rho_A=Tr_B(\rho_{AB})$ and $\rho_{AB}$ is the ground state density matrix. Does it mean that we can perform unitary operations localized near the boundary and make the ground state a product state of the form $\rho_{AB}^{'}=\rho_A^{'}\times \rho_B^{'}$ ?

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