In the study of many-body strongly interacting systems obtaining exact ground states and determining the phase diagram is a very challenging task. An alternative approach to understanding phases of matter is to consider prototypical wavefunctions. Such wavefunctions can then serve as an input for an “inverse method” approach for constructing parent Hamiltonians that have these wave functions as ground states. While for some wavefunctions exact parent Hamiltonians are known, they are difficult to find generically and will typically be of a very non-local nature.
In this talk, I will discuss our numerical studies aimed at constructing approximate local parent Hamiltonians. I will focus on a family of spin states that are obtained by a Gutzwiller projection of mean-field fermionic states, including both Fermi sea and BCS wavefunctions. I will present our results for one-dimensional systems and discuss the quality of the resulting approximate parent Hamiltonian on the range of the allowed interactions.
