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Reduced density-matrix functional theory: Correlation and spectroscopy.

S Di Sabatino1, J A Berger2, L Reining3

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This study evaluates approximations in reduced density-matrix functional theory (RDMFT) and GW methods for electron correlation. Neither method fully captures strong correlation effects in the Hubbard dimer model, especially concerning spectral functions and removal/addition energies.

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Accurate modeling of electron correlation is crucial for predicting material properties.
  • Reduced Density-Matrix Functional Theory (RDMFT) and GW approximation are key computational methods.
  • Understanding the limitations of these methods in strongly correlated systems is essential.

Purpose of the Study:

  • To assess approximations in RDMFT and GW for electron correlation.
  • To analyze the performance of these theories in calculating total energies, occupation numbers, removal/addition energies, and spectral functions.
  • To investigate the treatment of degeneracies and spin-symmetry breaking in RDMFT using the Hubbard dimer model.

Main Methods:

  • Utilized the exactly solvable Hubbard dimer model at 1/4 and 1/2 fillings.
  • Focused on the atomic limit to study strong electron correlation.
  • Compared RDMFT approximations with the GW approximation.
  • Analyzed results from both spin-singlet ground states and spin-symmetry broken cases.

Main Results:

  • Neither RDMFT nor GW approximations fully captured the signature of strong correlation from the spin-singlet ground state.
  • Both methods yielded exact results for the spin-symmetry broken case in the Hubbard dimer model.
  • Spectroscopic properties were shown to change significantly between different spin structures.

Conclusions:

  • Current approximations in RDMFT and GW struggle to accurately describe strong electron correlation effects in certain scenarios.
  • The treatment of spin-symmetry breaking is critical for correctly capturing the physics of strongly correlated systems.
  • Further development of theoretical methods is needed for robust predictions in complex electronic systems.