Quantum Many-Body Effects in X-Ray Spectra Efficiently Computed using a Basic Graph Algorithm

• Published in: arXiv.org
• Main Authors: Liang, Yufeng, Prendergast, David
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.01.2018
• Subjects: Algorithms; Bethe-Salpeter equation; Dependence; Determinants; Electronic structure; Electrons; Fermi liquids; Feynman diagrams; Fine structure; First principles; Mathematical analysis; Orthogonality; Physics - Materials Science; Search algorithms; Self consistent fields; Spectrum analysis; Transition metal oxides; Transition metals; X ray spectra
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1801.04073

The growing interest in using x-ray spectroscopy for refined materials characterization calls for accurate electronic-structure theory to interpret x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a non-diagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017)], we exploit the linear-dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of 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 that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.