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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Scrutinizing GW-Based Methods Using the Hubbard Dimer.

S Di Sabatino1,2, P-F Loos1, P Romaniello2

  • 1Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France.

Frontiers in Chemistry
|November 15, 2021
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Summary
This summary is machine-generated.

Full self-consistency resolves multiple quasiparticle solutions in the GW approximation. The Bethe-Salpeter equation (BSE) method accurately calculates correlation energies, especially with the trace formula, for the Hubbard dimer model.

Keywords:
GWadiabatic-connection fluctuation-dissipation theorembethe-salpter equationhubbard dimermultiple quasiparticle solutionstrace formula

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • The GW approximation is a key many-body perturbation theory method for electronic structure calculations.
  • Understanding quasiparticle properties and neutral excitations is crucial for predicting material behavior.
  • The Hubbard dimer model provides a simplified yet insightful system for analyzing theoretical approximations.

Purpose of the Study:

  • To investigate the behavior of the GW approximation and the Bethe-Salpeter equation (BSE) formalism within the Hubbard dimer model.
  • To analyze the impact of electron-electron interaction strength (U) on quasiparticle solutions and neutral excitation spectra.
  • To compare different methods for calculating correlation energies and assess their accuracy and stability.

Main Methods:

  • Utilized the symmetric Hubbard dimer model for theoretical analysis.
  • Employed the GW approximation, including one-shot, partially self-consistent, and fully self-consistent variants.
  • Applied the Bethe-Salpeter equation (BSE) formalism to study the neutral excitation spectrum.
  • Investigated correlation energy calculations using the trace (plasmon) formula and the adiabatic-connection fluctuation-dissipation theorem (ACFDT).

Main Results:

  • Full self-consistency in the GW approximation eliminates the issue of multiple quasiparticle solutions.
  • Neutral excitation energies can become complex with increasing electron-electron interaction (U), linked to approximate GW quasiparticle energies.
  • The BSE formalism with the trace formula accurately captures correlation energies across a broad range of U.
  • The trace formula shows sensitivity to complex excitation energies, while ACFDT is more stable but less accurate, especially for weak interactions.

Conclusions:

  • Full self-consistency is essential for robust quasiparticle predictions within the GW approximation.
  • The BSE formalism, particularly with the trace formula, offers an accurate route to correlation energies, despite potential complexities in excitation spectra.
  • The choice between trace formula and ACFDT depends on the desired balance between accuracy, stability, and the regime of electron-electron interaction.