Density matrix embedding theory: A one-electron reduced density matrix functional perspective

Speaker: Prof. Dr. Emmanuel Fromager
Institute: Laboratoire de Chimie Quantique de Strasbourg
Country: France
Speaker Link: https://lcqs.unistra.fr/staff-members/emmanuel-fromager/
Time: 15:00 CET 31-Jan-24

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:

[1] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012).
[2] S. Wouters, C. A. Jiménez-Hoyos, Q. Sun, and G. K.-L. Chan, J. Chem. Theory Comput. 12, 2706 (2016).
[3] S. Sekaran, M. Saubanère, and E. Fromager, Computation 2022, 10, 45.
[4] S. Sekaran, O. Bindech, and E. Fromager, J. Chem. Phys. 159, 034107 (2023).
[5] S. Sekaran, M. Tsuchiizu, M. Saubanère, and E. Fromager, Phys. Rev. B 104, 035121 (2021).
[6] S. Yalouz, S. Sekaran, E. Fromager, and M. Saubanère, J. Chem. Phys. 157, 214112 (2022).
[7] A. Georges and G. Kotliar, Phys. Rev. B 45, 6479 (1992).
[8] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
[9] F. Cernatic, S. Yalouz, and E. Fromager, in preparation (2023). 
[10] https://www.youtube.com/watch?v=mDkzmSJwwkQ&t=713s
[11] https://www.youtube.com/watch?v=8zgMa-MhoZg&t=19s

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