Large classes of quantum scarred Hamiltonians from matrix product states

The authors develop a general formalism to systematically construct parent Hamiltonians with quasiparticle excited states starting from a matrix product state (MPS) wave function. The resulting parent Hamiltonians are generically nonintegrable, and the quasiparticle excited states are thus examples of quantum many-body scars of the Hamiltonian. This method is used to recover well-known quantum scarred models, such as the AKLT spin chain, as well as to construct many new families of models, thus illustrating the close connection between parent Hamiltonians of MPS and quantum scarred models.