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Exchange-Correlation Energy from Green's Functions
Steven Crisostomo1, E K U Gross2, Kieron Burke1,3
1Department of Physics and Astronomy, <a href="https://ror.org/04gyf1771">University of California, Irvine</a>, California 92697, USA.
Physical Review Letters
|September 6, 2024
Summary
We present a new method to calculate density-functional theory (DFT) exchange-correlation energies using Green's functions. This approach offers a spectral view, separating single-particle and many-particle effects in quantum systems.
Area of Science:
- Quantum many-body physics
- Computational condensed matter physics
Background:
- Density-functional theory (DFT) excels at ground-state properties.
- Green's function methods, like GW, are standard for spectral functions.
- A gap exists in directly linking DFT exchange-correlation to Green's functions.
Purpose of the Study:
- To derive DFT exchange-correlation energy from Green's function formalism.
- To establish a spectral representation for DFT exchange-correlation.
- To provide an alternative to the fluctuation-dissipation theorem in DFT.
Main Methods:
- Utilizing the Galitskii-Migdal formula.
- Extracting exchange-correlation energy from Green's function.
- Developing a spectral representation of exchange-correlation.
Main Results:
- Successfully derived DFT exchange-correlation energy from Green's function.
- Demonstrated a spectral representation revealing distinct single-particle and many-particle contributions.
- Applied the method to the uniform electron gas and the two-site Hubbard model.
Conclusions:
- The spectral approach offers a novel perspective on DFT exchange-correlation.
- This method provides a bridge between Green's function techniques and DFT.
- The findings are applicable to various quantum many-body systems.
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