Bridging constrained random-phase approximation and linear response theory for computing Hubbard parameters

Abstract

The predictive accuracy of popular extensions to density-functional theory (DFT) such as DFT+U and DFT plus dynamical mean-field theory (DFT+DMFT) hinges on using realistic values for the screened Coulomb interaction U. Here, we present a systematic comparison of the two most widely used approaches to compute this parameter, i.e. linear response theory (LRT) and the constrained random-phase approximation (cRPA), using a unified framework based on the use of maximally localized Wannier functions. We show that the U in LRT and cRPA can differ as much as 30%. We demonstrate that this discrepancy arises from two main differences: neglecting the response of the exchange-correlation potential in cRPA and additional excitation channels in LRT. By taking these differences into account, we can achieve near perfect agreement between the two techniques. Moreover, we show that in cases with strong hybridization between interacting and screening subspaces, the application of cRPA becomes ambiguous and can lead to unrealistically small U values, while LRT remains well-behaved. Our work formally connects both methods, sheds light on their strengths and limitations, and emphasizes the importance of using a consistent set of Wannier orbitals to ensure transferability of U values between different implementations.

References in corpus (44)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Maximally localized Wannier functions: Theory and applications
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Quantum ESPRESSO toward the exascale
• Wannier90 as a community code: new features and applications
• Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems
• Frequency-dependent local interactions and low-energy effective models from electronic structure calculations
• Implementation of the Projector Augmented Wave LDA+U Method: Application to the Electronic Structure of NiO
• Calculations of Hubbard U from first-principles
• Hubbard parameters from density-functional perturbation theory
• Effective Coulomb interaction in transition metals from constrained random-phase approximation
• Screened Coulomb interaction in the maximally localized Wannier basis
• Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations
• Ab-initio procedure for effective models of correlated materials with entangled band structure
• Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps
• Screening of Coulomb interactions in transition metals
• RESPACK: An ab initio tool for derivation of effective low-energy model of material
• On the mechanism for orbital-ordering in KCuF3
• High-throughput determination of Hubbard U and Hund J values for transition metal oxides via linear response formalism
• Parameter-free hybrid functional based on an extended Hubbard model: DFT+U+V
• First-principles Calculation of Effective Onsite Coulomb Interaction of 3d Transition Metals: Constrained Local Density Functional Approach with Maximally Localized Wannier Function
• The role of spin in the calculation of Hubbard $U$ and Hund's $J$ parameters from first principles
• Efficient First-Principles Approach with a Pseudohybrid Density Functional for Extended Hubbard Interactions
• Dynamical screening in correlated electron systems - from lattice models to realistic materials
• d- and f-orbital correlations in the REFeAsO compounds
• On the limitations of cRPA downfolding
• Accuracy of downfolding based on the constrained random phase approximation
• Random Phase Approximation for gapped systems: role of vertex corrections and applicability of the constrained random phase approximation
• Renormalization of effective interactions in a negative charge-transfer insulator
• Orbital-resolved DFT+U for molecules and solids
• Importance of intersite Hubbard interactions in $\beta$-MnO${}_2$: A first-principles DFT+$U$+$V$ study
• Downfolding from Ab Initio to Interacting Model Hamiltonians: Comprehensive Analysis and Benchmarking of the DFT+cRPA Approach
• Rigorous screened interactions for realistic correlated electron systems
• Comparative study of first-principles approaches for effective Coulomb interaction strength $U_{\mathrm{eff}}$ between localized $f$-electrons: lanthanide metals as an example
• Explicit demonstration of the equivalence between DFT+U and the Hartree-Fock limit of DFT+DMFT
• Importance of ligand on-site interactions for the description of Mott-insulators in DFT+DMFT
• Oxygen Vacancies in Strontium Titanate: a DFT+DMFT study
• Interface tool from Wannier90 to RESPACK: wan2respack
• Calculation of screened Coulomb interaction parameters for the charge-disproportionated insulator CaFeO${}_3$
• Comparative analysis of methods for calculating Hubbard parameters using cRPA
• Strontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenate
• Constrained Random Phase Approximation: the spectral method