Abstract
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. The latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form , where is the integration in frequency of the trace operator. Here, we show that using a sum-over-poles representation for the Green's functions and the algorithmic-inversion method one can obtain, in full generality, an explicit analytical expression for . Further, this allows us (1) to recover an explicit expression for the random phase approximation correlation energy in the framework of the optimized effective potential and (2) to derive a variational expression for the Klein functional valid in the presence of an embedding bath.
- Received 12 September 2023
- Revised 10 April 2024
- Accepted 11 April 2024
DOI:https://doi.org/10.1103/PhysRevB.110.045149
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society