Self-Consistent Coulomb Interactions from Embedded Dynamical Mean-Field Theory

TL;DR

This work establishes a self-consistent, first-principles framework to determine the screened Coulomb interaction $U$ within embedded dynamical mean-field theory (eDMFT), incorporating vertex corrections through constrained DMFT (cDMFT) in the same many-body formalism used for electronic structure. By computing $U$ from local charging energies via $U_S - \alpha J_S = E[N+1] - 2E[N] + E[N-1]$ and treating all correlated sites in a supercell as quantum impurities except a central constrained one, the method yields self-consistent screening that reproduces experimental spectral functions across wide 3$d$–5$d$ materials, including metals, Mott insulators, and altermagnets. The cDMFT-$U$ values are systematically larger than those from cDFT or cRPA, with a distinct separation between metals and insulators and enhanced transferability within material families, thereby improving the predictive power of DFT+DMFT and its extensions. Across NiO, V$_2$O$_3$, MnTe, FeSe, RuO$_2$, SrIrO$_3$, and related compounds, the approach achieves excellent agreement with photoemission and ARPES data, capturing metal–insulator transitions and correlation-driven features that static schemes miss. This framework provides a robust, unified route for determining effective Coulomb interactions from first principles in strongly correlated materials.

Abstract

We develop a self-consistent first-principles framework for determining the screened Coulomb interaction strength (U) based on constrained dynamical mean-field theory (cDMFT). Unlike conventional approaches, this method incorporates essential vertex corrections within the same embedded-DMFT formalism used for the electronic structure calculation. Using the cDMFT-derived interaction strengths as input to embedded DMFT yields spectral functions in excellent agreement with photoemission experiments across a wide range of materials, spanning 3d to 5d transition-metal compounds, including correlated metals, Mott insulators, altermagnets, and unconventional superconductors. This unified many-body framework establishes a systematic first-principles route for determining interaction strengths in correlated materials and substantially enhances the predictive power of DFT+DMFT and its extensions.

Figures (7)

• Figure 1: Schematic representations of (a) cDFT, (b) cRPA, and (c) proposed cDMFT methods.
• Figure 2: Application of cDMFT method for various 3$d$ metals and insulators. (a) Spectral functions comparison of La$_3$Ni$_2$O$_7$ between eDMFT (II & III) and experiment (I & IV) LNO_exp_yang2024. The bandwidths are marked by double sided arrow. Thin green lines denote the band structures obtained from DFT+$U$ calculations. (b) eDMFT computed spin and momentum resolved spectral functions of MnTe (I & III) compared with the experimental ARPES spectra (II and IV) PRB_MnTe_exp. In computed spectra, the minority (majority) electrons are denoted by red (blue) color. The green solid (black dotted) lines represent the spin-up (spin-down) bands from DFT+$U$ computation. (c) Crystal structures (I and II) and spectral functions comparisons (III and IV) of V$_2$O$_3$ in $\alpha$ and $\beta$ phases to show the metal-insulator transition. Experimental spectra are taken from Ref. v2o3_exp_MIT_sciadv. DFT+$U$ bands are marked with green lines. (d) Site dependent projected density of states (PDOS) of Ni-3$d$ orbitals in a 2$\times$2$\times$2 supercells for N+1, N and N-1 constrained electrons are plotted for two different distances (' OA' and ' OB') from origin (' O'), showing appearance of the Kondo peak near E$_F$, which is marked by a green box.
• Figure 3: Comparison of spectral functions obtained from (a) eDMFT in the paramagnetic phase and (b) ARPES measurements of 4$d$-metallic RuO$_2$ (reproduced from Ref. ruo2_exp_fedchenko2024). The green lines in (a) denote the dispersion obtained from DFT+$U$ calculations.
• Figure 4: Momentum resolved spectral functions from eDMFT for (a) SrIrO$_3$ and (b) Sr$_2$IrO$_4$. ARPES data (green) and the second derivative data (lime green) of (a) SrIrO$_3$ and (b) Sr$_2$IrO$_4$ are reproduced from nie2015interplay for comparison.
• Figure 5: Orbital-resolved imaginary part of self-energy in Matsubara frequency ($i\omega$) for (a) $\alpha$-V$_2$O$_3$ in metallic phase and (b) $\beta$-V$_2$O$_3$ in insulating phase.