Progress toward a formal functional theory of strongly correlated systems

We explore the hypercomplex Kohn-Sham (HCKS) formalism and develop a third exact functional theory beyond the popular Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT), called 1-HCKS. The orbitals of hierarchical correlation introduced in 1-HCKS are interesting because their occupations are neither necessarily integers, as in KS-DFT, nor overly flexible, as in RDMFT; rather, they can capture strong correlation with fractional occupations, governed by stringent constraints. This feature allows 1-HCKS to combine the advantages of KS-DFT and RDMFT in dealing with dynamic correlation and strong correlation, while eliminating the issues of computational convergence and basis set dependence encountered in RDMFT. Thus, 1-HCKS is a promising alternative for implementing DFT beyond KS-DFT, especially for the treatment of strongly correlated systems.