Taming Convergence in the Determinant Approach for X-Ray Excitation Spectra

Abstract

A determinant formalism in combination with \emph{ab initio} calculations proposed recently has paved a new way for simulating and interpreting x-ray excitation spectra. The new method systematically takes into account many-electron effects in the Mahan-Noziéres-De Dominicis (MND) theory, including core-level excitonic effects, the Fermi-edge singularity, shakeup excitations, and wavefunction overlap effects such as the orthogonality catastrophe, all within a universal framework using many-electron configurations. A heuristic search algorithm was introduced to search for the configurations that are important for defining spectral lineshapes, instead of enumerating them in a brute-force way. The algorithm has proven to be efficient for calculating \ce{O} $K$ edges of transition metal oxides, which converge at the second excitation order (denoted as $f^{(n)}$ with $n=2$), i.e., the final-state configurations with two \emph{e-h} pairs (with one hole being the core hole). However, it remains unknown how the determinant calculations converge for general cases and at which excitation order $n$ one should stop the determinant calculation. Even with the heuristic algorithm, the number of many-electron configurations still grows exponentially with the excitation order $n$. In this work, we prove two theorems that can indicate the order of magnitude of the contribution of the $f^{(n)}$ configurations, so that one can estimate their contribution very quickly without actually calculating their amplitudes. The two theorems are based on the singular-value decomposition (SVD) analysis, a method that is widely used to quantify entanglement between two quantum many-body systems. We examine the $K$ edges of several metallic systems with the determinant formalism up to $f^{(5)}$ to illustrate the usefulness of the theorems.

References in corpus (22)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Multiplet ligand-field theory using Wannier orbitals
• X-ray Absorption Near-Edge Structure calculations with pseudopotentials. Application to K-edge in diamond and alpha-quartz
• A deterministic alternative to the full configuration interaction quantum Monte Carlo method
• Bethe-Salpeter Equation Calculations of Core Excitation Spectra
• Induced magnetism of carbon atoms at the graphene/Ni(111) interface
• Angular dependence of core hole screening in LiCoO2: A DFT+U calculation of the oxygen and cobalt K-edge x-ray absorption spectra
• Accurate X-Ray Absorption Predictions for Transition Metal Oxides: An Advanced Self-Consistent-Field Approach Inspired by Many-Body Perturbation Theory
• Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set
• Systematic computation of crystal field multiplets for X-ray core spectroscopies
• Using RIXS to uncover elementary charge and spin excitations in correlated materials
• Exact diagonalization results for resonant inelastic x-ray scattering spectra of one-dimensional Mott insulators
• K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects
• Doping Evolution of Oxygen K-edge X-ray Absorption Spectra in Cuprate Superconductors
• Quantum Many-Body Effects in X-Ray Spectra Efficiently Computed using a Basic Graph Algorithm
• Vibrational Effects in X-ray Absorption Spectra of 2D Layered Materials
• Non-perturbative series expansion of Green's functions: The Anatomy of Resonant Inelastic X-Ray Scattering in Doped Hubbard Model
• Specific many-electron effects in X-ray spectra of simple metals and graphene

Cited by in corpus (5)

• Density Functional Theory for Electronic Excited States
• Equation of motion coupled-cluster approach for intrinsic losses in x-ray spectra
• Description of resonant inelastic x-ray scattering in correlated metals
• Changes in polarization dictate necessary approximations for modeling electronic de-excitation intensity: an application to X-ray emission
• CleaRIXS: A Fast and Accurate First-Principles Method for Simulation and Analysis of Resonant Inelastic X-ray Scattering