## Prof. Dr Emmanuel Fromager

*Laboratoire de Chimie Quantique, Institut de Chimie, University Strasbourg, France*

Density matrix embedding theory (DMET) [1] is a promising approach for the description of strongly correlated electrons in both extended and molecular systems [2]. Its basic idea is to embed the fragment of interest (which consists of localised orbitals) in the system under study into a one-electron quantum bath, *i.e. *a set of orbitals (which are delocalised over the full system) whose number usually equals the number of fragment orbitals. After a thorough presentation of DMET in the special case of non-interacting or mean-field electrons, where the approach is exact, as well as its formal connection to density functional theory [3], standard implementations of the approach for correlated electrons will be discussed, with a particular focus on the (one-electron reduced) density matrix functional construction of the bath [4] and the various approximations that are made [5,6]. In the latter case, mapping a correlated embedded fragment density matrix onto a (full-size) non-interacting system, which is a standard procedure inspired by dynamical mean-field theory (DMFT) [7,8], raises serious representability issues. Using an enlarged bath is an appealing practical solution which, as we will see, can be related to the description of electron correlation at the full-size level within a given active orbital space [9]. Another way to reduce the ill-conditioned mapping constraint of DMET, which is more exotic and currently under investigation, relies on an indirect mapping of the density matrix onto a non-interacting but non-Hermitian system [10]. The relevance of such an approach will be discussed in the light of the anti-Hermitian contracted Schrödinger equation [11].

**Keywords:** density matrix, embedding theory

## References:

*J. Chem. Phys. 159, 034107 (2023).*