A quantum embedding approach to density-functional approximations for many-electron ensembles

Density matrix embedding theory (DMET) [1] has recently been reformulated in terms of a unitary Householder transformation that is applied to a full-size (usually idempotent) ground-state one-electron reduced density matrix [2]. On that basis, a formally exact connection between DMET and density-functional theory (DFT) has been established for the Hubbard model [3]. In this context, the idempotency of the Kohn-Sham (KS) density matrix yields a closed embedding cluster made of as many bath orbitals as embedded fragment orbitals [4]. In this talk, an extension of the embedding procedure to bi-ensembles of ground and singly-excited states will be presented. In particular, we will show that, in spite of the non-idempotency of the ensemble KS density matrix, a closed (but enlarged) embedding cluster can still be designed through successive Householder transformations. Proof-of-concept results obtained with a finite one-dimensional Hubbard system will be shown. Extensions to higher excitations will also be discussed.

[1] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012).

[2] S. Sekaran, M. Tsuchiizu, M. Saubanère, and E. Fromager, Phys. Rev. B 104, 035121 (2021).

[3] S. Sekaran, M. Saubanère, E. Fromager, Computation, 10(3), 45 (2022).

[4] S. Yalouz, S. Sekaran, E. Fromager, and M. Saubanère, arXiv:2209.10302 (2022).