Tripartite entanglement and 2D tensor network states

2D tensor network states have recently become valuable for solving ground states of strongly interacting Hamiltonians and for simulating quantum devices. However, the expressive power of 2D tensor network state is still an open problem, and it can be costly to extract physical observables from a tensor network state. Entanglement area law is a necessary condition for the application of tensor network algorithms, but not a sufficient condition. In this talk, I will give a sufficient condition for efficiently computable 2D tensor network states via tripartite entanglement, and discuss the hierachy of tripartite entanglement for typical physical states.