Abstract

The use of functionals of compact quantities, such as Green’s functions, the one-body reduced density matrix, or the density, is a powerful alternative to wavefunction-based methods. In this talk, we will start from general strategies that are common to different approaches relying on functionals, briefly discussing ideas and major concepts. We will investigate the difficulties of finding good approximations, and highlight some strategies for improvement that allow us to consider Density Functional Theory, Many-Body Perturbation Theory, and Dynamical Mean Field Theory on the same footing. In particular, we will concentrate on the way in which models make first principles electronic structure calculations feasible. This relies on powerful methods, including wavefunction-based ones, to provide benchmarks1, and to solve the models. One of the most prominent models is the homogeneous electron gas, whose spectroscopic properties still have to be explored. We will illustrate this point by discussing electron-hole interaction effects in the low-density regime2, comparing to the more familiar excitonic effects in semiconductors and insulators3. We will then discuss how one may use models in a well defined and systematic way4,5, in order to design new classes of functionals.

References 1. A. Aouina, M. Gatti, S. Chen, S. Zhang, and L. Reining, Phys. Rev. B 107 , 195123 (2023) 2. J. Koskelo, L. Reining and M. Gatti, https://arxiv.org/abs/2301.00474 3. V. Gorelov, L. Reining, M. Feneberg, et al., npj Comput Mater 8, 94 (2022) 4. M. Vanzini, A. Aouina, M. Panholzer, M. Gatti, and L. Reining, npj Comput Mater 2022, 8, 98 5. A. Aouina, M. Gatti, and L. Reining, Faraday Discussions 2020, 224, 27