Householder transformed density matrix functional embedding theory.

Single-impurity quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of DMET, we use in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the bath is interacting, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling and no density-driven Mott-Hubbard transition is observed. These flaws originate from the fact that, in the exact theory, the Householder cluster is an open subsystem. Extending Ht-DMFET to multiple impurities via a block-Householder transformation is a natural follow-up to this work. Connections with density/density matrix functional theories should also be explored. Work is currently in progress in these directions.