Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals

The recently proposed Householder transformed density-matrix functional embedding theory (Ht-DMFET) [Sekaran et al., Phys. Rev. B 104, 035121 (2021)], which is equivalent to (but formally simpler than) density matrix (DMET) in the non-interacting case, revisited from perspective of density-functional (DFT). An in-principle-exact version Ht-DMFET derived for one-dimensional Hubbard lattice with a single embedded impurity. On basis well-identified approximations, local potential (LPFET) formulated and implemented. Even though LPFET performs better than low-density regime, particular when electron correlation strong, both methods are unable describe density-driven Mott-Hubbard transition, as expected. These results combined our exact reveal that statically impurity can principle gap opening, provided complementary (that describes interaction cluster its environment, simply neglected LPFET) exhibits derivative discontinuity (DD) at half filling. extension multiple impurities (which would enable circumvent modeling DDs) generalization quantum chemical Hamiltonians left future work.