Understanding effective model derivation for an Fe_Al⁰ point defect in AlN using ab-initio quantum Monte Carlo calculations

In point defect physics, simplified representations of Hamiltonians aid in materials design for optoelectronics and quantum information [1]. A common approach to deriving effective models for solid-state systems is downfolding from a density functional theory (DFT) electronic structure to a minimal active space, where interactions are screened in the constrained random phase approximation (cRPA) [2]. However, DFT+cRPA involves approximations such as assumption of static screening and choice of double counting correction, which can lead to models with incorrect eigenstates: as shown for an Fe_Al⁰ defect in AlN [2].



Leveraging high-accuracy ab-initio quantum Monte Carlo (QMC) calculations [3], we diagnose errors in downfolded models for Fe_Al⁰:AlN from DFT+cRPA using several standard methods. In particular, we examine errors in the effective models’ eigenstates and terms. Using the detailed QMC data, we determine that the one-particle terms are very sensitive to the reference DFT state and that double-counting corrections can drive the effective Hamiltonian into an unphysical regime. Beyond the one-particle terms, it appears that static-limit cRPA overestimates anisotropy in the interaction terms.



[1] M. Bockstedte, et. al., npj. Quantum Mater. 3 31 (2018).

[2] L. Muechler, et. al., Phys. Rev. B 105 235104 (2022).

[3] W. M. C. Foulkes, et. al., Rev. Mod. Phys. 73, 33 (2001).