Method to identify parent Hamiltonians for trial states

We describe a general method to identify exact, local parent Hamiltonians for trial states such as quantum Hall or spin-liquid states, which we have used extensively during the past decade. It can be used to identify exact parent Hamiltonians, either directly or via the construction of simpler annihilation operators from which a parent Hamiltonian respecting all the required symmetries can be constructed. Most remarkably, however, the method provides approximate parent Hamiltonians whenever an exact solution is not available within the space of presumed interaction terms.