PI: Nicola Colonna (PSI)
January 1, 2025 – December 31, 2027
We have recently achieved a significant breakthrough in the treatment of correlated electrons [1,2] , where dynamical (i.e., frequency-dependent) functionals can be used, at variance with the diagrammatic approaches of many-body perturbation theory or dynamical mean-field theory. A key element is the introduction of sums over poles to represent all propagators (self-energies, Green’s function) and a numerically exact algorithm to solve the Dyson equation that is closed with respect to the class of sum-over-poles propagators [3].
The aim of this project is to implement and deploy this formulation to complex accelerated hardware architectures, as present in Alps (NVIDIA Grace-Hopper), LUMI (AMD Epyc and Instinct), and in future pre- and exascale machines, to calculate efficiently the spectral properties of correlated materials. Broadly speaking, spectral properties encode the response of a material to external stimuli, and they are of the utmost relevance in fundamental science and applied technologies: typical examples are photoemission spectra (widely used in recent years to characterise topological properties), electronic transport (for information-and-communication technologies), light absorption (for energy harvesting) or emission (for quantum technologies). While important in general, accessing the spectral properties of correlated materials is even more so as quantum materials typically exhibit diverse many-body and topological phenomena, which not only challenge our physical understanding but also present opportunities for next-generation technologies. The spectral properties of a material are most notably exemplified by its electronic band structure, that captures the charged excitations of the many-body electronic system. These can be correctly described by advanced electronic-structure methods relying on dynamical formulations based on Green’s function theory; typical examples are many-body perturbation theory [4] (e.g., in the GW approximation), dynamical mean-field theory [5,6] (DMFT), and many embedding approaches (e.g., quantum-defect embedding theory [7], or QDET).
A general feature of functional and diagrammatic approaches to spectroscopies is the appearance of frequency-dependent effective interactions that arise from the dynamical screening of the bare Coulomb interaction. The ab-initio evaluation of these effective interactions requires to calculate the interacting response function in the frequency domain and, most often, in a localized manifold (e.g., atomic projectors or maximally localized Wannier functions (MLWFs)), and represents one of the computational bottlenecks of these simulations. So, the core goal of this project is to calculate these dynamical response functions on accelerated architectures, extending the recent achievements in developing the static response functions (e.g., for Koopmans and Hubbard functionals) that have taken place within the PASC program; these quantities can be used in many other electronic-structure methods (e.g., dynamical mean-field theory or adiabatic connection DFT), but here will see their full power as providing the core ingredient for dynamical functionals.
[1] Chiarotti et al., Phys. Rev. Research 6, L032023 (2024)
[2] Vanzini, and Marzari, ArXiv:2309.12144 (2023)
[3] Chiarotti et al., Physical Review Research 4 (1), 013242 (2022)
[4] Onida et al., Review Modern Physics 74, 601–659 (2002)
[5] Georges et al., Reviews of Modern Physics 68 (1), 13–125 (1996)
[6] Kotliar et al., Reviews of Modern Physics 78 (3), 865–951 (2006)
[7] Ma et al., Journal of Chemical Theory and Computation 17 (4), 2116–2125 (2021)