Bridging Constrained Random-Phase Approximation and Linear Response Theory for Computing Hubbard Parameters

Area of Science:

• Condensed Matter Physics
• Computational Materials Science
• Quantum Chemistry

Background:

• Density-functional theory (DFT) extensions like DFT+U and DFT+DMFT require accurate screened Coulomb interaction (U) values.
• The predictive power of these methods depends heavily on the reliability of the computed U parameter.

Purpose of the Study:

• To systematically compare the linear response theory (LRT) and constrained random-phase approximation (cRPA) methods for calculating the screened Coulomb interaction (U).
• To identify the sources of discrepancies between LRT and cRPA and to establish conditions for their agreement.
• To investigate the behavior of both methods in cases of strong hybridization and their impact on U values.

Main Methods:

• Utilized a unified computational framework employing maximally localized Wannier functions.
• Performed a systematic comparison of LRT and cRPA calculations for the screened Coulomb interaction (U).
• Analyzed the contributions of exchange-correlation potential response and excitation channels to discrepancies.

Main Results:

• Found significant differences (up to 30%) in U values calculated by LRT and cRPA, even in unambiguous cases.
• Identified the neglect of exchange-correlation potential response in cRPA and additional excitation channels in LRT as primary causes for discrepancies.
• Demonstrated that accounting for these differences leads to near-perfect agreement between LRT and cRPA.
• Observed that cRPA can yield ambiguous and unrealistically small U values in strongly hybridized systems, while LRT remains robust.

Conclusions:

• Formally connected LRT and cRPA, clarifying their respective strengths and limitations in calculating the screened Coulomb interaction (U).
• Highlighted the importance of considering the response of the exchange-correlation potential and all relevant excitation channels for accurate U calculations.
• Emphasized the necessity of using consistent Wannier orbitals for transferable U values across different computational implementations.