[Paper Review] Dynamical local connector approximation for electron addition and removal spectra

M. Vanzini, Lucia Reining+1 more|arXiv (Cornell University)|Aug 8, 2017

Electronic and Structural Properties of Oxides2 references3 citations

TL;DR

This paper introduces the dynamical local connector approximation (dynLCA), a computationally efficient method to calculate electron addition and removal spectra using a local, frequency-dependent, real spectral potential derived from the homogeneous electron gas (HEG). The approach achieves accuracy comparable to GW calculations at a cost similar to LDA, significantly improving band structures and spectral functions across metals, semiconductors, and insulators.

ABSTRACT

Realistic calculations of electron addition and removal spectra rely most often on Green's functions and complex, non-local self-energies. We introduce a shortcut to obtain the spectral function directly from a local and frequency-dependent, yet real, potential. We calculate this potential in the homogeneous electron gas (HEG), and we design a connector which prescribes the use of the HEG results to calculate spectral functions of real materials. Benchmark results for several solids demonstrate the potential of our approach.

Motivation & Objective

• To develop a practical shortcut for calculating spectral functions without solving the full non-local, frequency-dependent self-energy in many-body perturbation theory.
• To overcome the computational inefficiency of standard Green's function approaches that require evaluation of the full non-local self-energy.
• To demonstrate that a local, real, frequency-dependent spectral potential—derived from the HEG—can yield accurate spectral functions for real materials.
• To provide a feasible alternative to GW and spectral functional theory by using a simplified connector based on HEG results.
• To validate the method across diverse materials, including metals, semiconductors, and insulators, showing improved accuracy over LDA with minimal computational overhead.

Proposed method

• The method constructs a local, frequency-dependent spectral potential (SP) using results from the homogeneous electron gas (HEG), obtained via the generalized Sham-Schlüter equation.
• The SP is built using a dynamical local connector approximation (dynLCA), which combines the HEG's frequency-dependent xc contribution with the local density functional potential from DFT.
• The spectral function is computed via the Dyson equation using the SP, with the key innovation being the use of a real, local potential instead of a non-local, complex self-energy.
• The method uses the HEG's quasiparticle energies and spectral weights as a reference to calibrate the SP, ensuring consistency with high-accuracy GW-like results.
• For the spectral function, the method employs a band structure-based expression (Eq. 7) that sums delta functions over eigenenergies of the SP, improving accuracy over the standard Green's function trace.
• The approach is implemented using a simple prescription: the SP is constructed as a sum of the LDA exchange-correlation potential and a frequency-dependent correction derived from the HEG, with parameters tabulated for different rs values.

Experimental results

Research questions

• RQ1 Can a local, real, and frequency-dependent spectral potential be constructed from the homogeneous electron gas to accurately describe electron addition and removal spectra in real materials?
• RQ2 Does the dynamical local connector approximation (dynLCA) achieve spectral function accuracy comparable to GW calculations while maintaining computational efficiency similar to LDA?
• RQ3 How well does the method perform across materials with varying electronic inhomogeneity, such as metals, semiconductors, and wide-gap insulators?
• RQ4 Can the SP derived from the HEG be used to improve both the band structure and spectral function beyond standard LDA, especially in systems with strong electron correlation or band gap errors?
• RQ5 What is the role of the DFT exchange-correlation potential in the connector, and how does it affect the accuracy in non-metallic and inhomogeneous systems?

Key findings

• For sodium (Na), a metal, the dynLCA spectral function shows excellent agreement with the HSE06 reference, with accurate band dispersion and peak positions.
• For aluminum (Al), a less homogeneous metal, the dynLCA method also yields highly accurate spectral functions, demonstrating robustness beyond simple metals.
• In silicon (Si), a semiconductor, the dynLCA reduces the bandwidth error from 10% (LDA) to 1% (13.11 eV) and the gap error from 53% (LDA) to 35% (0.78 eV), significantly improving over LDA.
• For argon (Ar), a wide-gap insulator, the method reduces the gap error from 22% (LDA) to just 0.9% (10.85 eV) and the bandwidth error from 8.3% to 0.06%, showing exceptional performance in insulators.
• The computational cost of dynLCA is similar to LDA and more than an order of magnitude lower than HSE06, making it highly efficient for practical applications.
• The method improves the band structure beyond LDA, enabling potential use in angle-resolved photoemission spectroscopy, and provides a viable alternative to GW for spectral function calculations.