Self-consistent second-order Green’s function perturbation theory for periodic systems
Abstract
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. Here, by analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.
- Publication Date:
- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1843753
- Alternate Identifier(s):
- OSTI ID: 1236723
- Grant/Contract Number:
- SC0010381; ER16391
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 144; Journal Issue: 5; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Spectral phenomena and properties; Density-matrix; Insulators; Electronic correlation; Ab-initio methods; Molecular structure; Perturbation theory; Dyson-Schwinger equation; Crystal lattices; Green-functions technique
Citation Formats
Rusakov, Alexander A., and Zgid, Dominika. Self-consistent second-order Green’s function perturbation theory for periodic systems. United States: N. p., 2016.
Web. doi:10.1063/1.4940900.
Rusakov, Alexander A., & Zgid, Dominika. Self-consistent second-order Green’s function perturbation theory for periodic systems. United States. https://doi.org/10.1063/1.4940900
Rusakov, Alexander A., and Zgid, Dominika. Wed .
"Self-consistent second-order Green’s function perturbation theory for periodic systems". United States. https://doi.org/10.1063/1.4940900. https://www.osti.gov/servlets/purl/1843753.
@article{osti_1843753,
title = {Self-consistent second-order Green’s function perturbation theory for periodic systems},
author = {Rusakov, Alexander A. and Zgid, Dominika},
abstractNote = {Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. Here, by analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.},
doi = {10.1063/1.4940900},
journal = {Journal of Chemical Physics},
number = 5,
volume = 144,
place = {United States},
year = {Wed Feb 03 00:00:00 EST 2016},
month = {Wed Feb 03 00:00:00 EST 2016}
}
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