Low-energy effective model for H₄ square molecule derived from ab initio calculations

Effective model Hamiltonians are the workhorse of the study of complex electronic states. Typically these models are some degree of phenomenological, in that they are justified based on their agreement with experimental results. However, as models become more complex, this comparison becomes difficult to make in a systematic way. On the other hand, it is now possible to perform many-body quantum calculations to high accuracy for systems with ab initio Hamiltonians and up to hundreds of electrons. These calculations give key insights into correlated electron physics at that scale.

We rigorously examine effective model Hamiltonians for the purely theoretical H₄ square molecule, using exact ab initio calculations as a data source. We explicitly construct a 1-1 mapping between a single-band model and the infinite dimensional low-energy ab initio space. Renormalization of operators such as double occupancy are derived as a part of the process. We find that such operator renormalization is key to obtaining simple and accurate models from first principles.