 Affleck--Kennedy--Lieb--Tasaki parent Hamiltonian

The AKLT parent Hamiltonian is $H={\sum }_j{P}_{j,j+1}^{(2)}$, where $P^{(2)}$ projects two neighboring spin-one particles onto total spin two. It is frustration free, and the periodic AKLT MPS is its unique ground state on a sufficiently long chain.