Entropy functional approach for Fermionic lattice models

We formulate an entropy functional of a particular subset of reduced density matrix (RDM) for interacting Fermionic lattice models, which includes all local elements of the RDM (ie. all local N-body contributions); while the only nonlocal contributions are confined to the single-particle density matrix. We propose dual symmetric approximations for the unknown entropy functional (i.e. the value and domain) and evaluate it as compared to numerically exact or highly accurate ground state properties (i.e. Hubbard models in 0d, 1d, 2d, d=inf). Our approach is sufficiently precise in both low dimensional and high dimensional systems, as compared to approaches such as density matrix renormalization group and dynamical mean-field theory; which are numerically exact in one limit and inapplicable or unreliable in the other. Furthermore, our approach has a relatively small computational cost and could be highly applicable in the context total energies of strongly correlated materials and molecules.