Tackling Quantum Many-Body Problems in X-Ray Spectra via a Basic Graph Algorithm

The growth in access to detailed materials characterization using X-ray spectroscopy highlights the need for more accurate electronic-structure theory predictions of X-ray absorption near-edge fine structure.
In this talk, we introduce an efficient and unified framework to exactly incorporate all the many-electron processes in a Fermi liquid upon sudden perturbation by a potential (such as a core hole).
We start with a determinant formalism for the many-electron transition amplitudes [Phys. Rev. Lett. 118, 096402 (2017)],
and find that an elementary graph algorithm, breadth-first search, can be introduced to quickly identify the determinants that are significant for spectral calculation, removing the necessity to evaluate many vanishingly small terms.
This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path finding process.
We demonstrate the efficiency and practicality of the new approach over a class of solid-state transition metal oxides, whose electronic structure is described using density functional theory with on-site Coulomb interactions provided by Hubbard-$U$ corrections.