Session N58: Quantum Embedding Methods: Materials

Model self-energies for dynamical correlations in transition-metal monoxides

Dynamical correlations beyond static mean-field are of fundamental importance in describing the electronic structure of complex materials like transition-metal oxides, where the low-energy physics is dominated by the interactions between partially filled, very localized d or f shell orbitals. To understand the interplay between screening and localization, high-level and computationally expensive theories such as DFT+DMFT or GW+EMDFT are often required. Given the complexity of these methods, actual calculations require expensive numerical implementations that may also hinder the interpretation of the underlying physics or limit the number of orbitals that can be treated as correlated. Motivated by the success of a recent approach to study local correlations in metals via a simple dynamical self-energy, in this work we propose its generalization to spin-polarized cases, and apply this framework to the study of the antiferromagnetic insulating phases of transition-metal monoxides MnO, FeO, CoO and NiO, considered as prototypical materials for beyond-DFT approaches.   

Self-consistent quantum defect embedding theory

Quantum Defect Embedding theory (QDET) [1-3] is a many-body embedding scheme to describe strongly correlated electrons localized within a given region of a solid, for example the electronic states of spin defects in semiconductors and insulators. Despite several successes of QDET in describing the electronic properties of point-defects, this framework becomes inaccurate when a large hybridization exists between the electronic states of the bulk and those of the defect, or when the effective screened interaction of the active space is frequency dependent. We present a method to solve these problems, which includes a self-consistent treatment of the host and the defect through the iterative computation of the screening in the active space and in the entire system. We then demonstrate its accuracy by comparing QDET results with those of other embedding methods and accurate chemical solvers for defective clusters. Our approach retains the scalability of QDET to large systems and paves the way to compute total-energies and to perform structural optimizations of excited states.

[1] H. Ma, M. Govoni, and G. Galli, npj Comput. Mater. 6, 85 (2020).

[2] N. Sheng et al., J. Chem. Theory Comput. 18, 3512 (2022).

[3] C. Vorwerk et al., Nat. Comput. Sci. 2, 424 (2022).   

Energies and spectra of solids from dynamical Hubbard functionals and the algorithmic-inversion method

Energy functionals of the Green's function can provide simultaneously spectral and thermodynamic properties of systems of interacting electrons.  We recently introduced [1] an approximation to the exchange-correlation part of the Klein functional that generalizes the DFT+U Hubbard energy functional to host a dynamical screened potential U(ω). Furthermore, we solve the resulting Dyson equation using the algorithmic-inversion method to access both spectral and thermodynamic quantities [1]. In this work, we present the self-consistent implementation of the framework and apply it to study the spectral, thermodynamic, and vibrational properties of SrVO₃.   

DFT + embedded DMFT Study of Doped Rare-Earth Nickelates

Doped rare-earth nickel-oxide compounds have continued to garner interest since they were discovered to be superconducting [1]. Among several theoretical studies, a recent advancement [2] is the proposal of a correlation-temperature phase diagram for the undoped parent compound RNiO₂ (R = La, Nd); this exhibits a high-temperature Curie-Weiss regime, a regime wherein Ni-d moments are partially screened at intermediate temperatures, and a fully screened low-temperature Fermi liquid regime as the ground state. To study the effects of doping on the phase diagram boundaries and on the electronic properties of the ground state, we perform self-consistent density functional theory (DFT) and embedded dynamical mean-field theory (eDMFT) calculations on La_1-xSr_xNiO₂, for a range of doping (x). We construct appropriate supercells for various dopings and find significant changes in the density of states for sufficiently large doping. Additionally, we examine the effects of doping on the projected band structure for the Ni-d electrons. We also discuss results from our eDMFT calculations.

1. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Nature 572, 624 (2019).

2. G. L. Pascut, L. Cosovanu, K. Haule, K. F. Quader, Comm Phys 6, 45 (2023).   

Design Decisions in the Creation of Parameter Free Embedding Theories

The development of parameter-free Quantum Embedding methods for the simulation of real materials requires design decisions ranging from the choice of spatial basis functions to the choice of quantum impurity solver. This general overview talk will highlight some of the design decisions behind popular choices and their associated costs and benefits; illustrate the presence of `hidden' free parameters where they exist, and motivate the need for future algorithmic development needed to advance the field. A route towards systematically improvable parameter-free adaptive simulations of quantum materials is outlined.   

Understanding effective model derivation for an FeAl0 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).   

Computing the Hall conductivity of strained Sr2RuO4

Transport is an important probe of quantum materials. Recent experiments revealed an intriguing dependence of the Hall conductivity of Sr2RuO4 on uniaxial strain [1]. Using a simple tight-binding model, the behavior of the Hall number under strain was related to that of the scattering rates [1]. Here, we compare these predictions to a many-body calculation using density functional theory, dynamical-mean-field theory, and the numerical renormalization group, similarly as in Ref. [2]. We also discuss how, generally, the Hall conductivity can be computed in correlated multiband systems.

[1] P.-Y. Yang, H. M. L. Noad, M. E. Barber, N. Kikugawa, D. Sokolov, A. P. Mackenzie, C. W. Hicks, Phys. Rev. Lett. 131, 036301 (2023)

[2] F. B. Kugler, M. Zingl, H. U. R. Strand, S.-S. B. Lee, J. von Delft, A. Georges, Phys. Rev. Lett. 124, 016401 (2020)   

Comparison of Quantum Embedding Methods on Fe Impurity in AlN

The ongoing development of quantum embedding methods, particularly that of density matrix embedding theory (DMET) [1] and quantum defect embedding theory (QDET), [2] has established this class of techniques as a promising approach for describing the excited states of point defects in solids. However, the various embedding methods each rely on their own sets of approximations and systematic comparisons of different approaches remain scarce. Furthermore, certain classes of defects such as transition metal defects in semiconductors are relatively less explored with embedding theories and recent research has suggested they may be a challenging test of such methods’ predictive power.[3] In this work, we apply both DMET with the Pyscf code and QDET as implemented within the West code to the Fe impurity in AlN, systematically assessing the influence of methodological parameters and comparing vertical excitation energy predictions.

 

[1] A. Mitra et al. J. Phys. Chem Lett. 12, 11688 (2021).

 

[2] Sheng et al. J. Chem. Theory Comput. 18, 3512 (2022).

 

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

Understanding the many-body electronic structure of the nitrogen-vacancy center in diamond

Understanding the behavior of the ground and excited states of the negatively charged nitrogen vacancy center (NV^-) in diamond under pressure is of fundamental interest to probe superconductivity in diamond anvil cells. The nature of the ground (³A₂ triplet) state and of photoluminescence signals were first identified using optically detected magnetic resonance,  however the symmetry and position of the singlet energies with respect to the ground state are still under debate. In the present work, we combine first-principle generalized DFT calculations with an in-house extended Hubbard model to describe the defect many-body energy states. Using DFT-HSE06 and the ΔSCF method, we performedcalculations of the ground state and of some excited states total energies, which we used to parameterize our Hubbard model. Inclusion of interactions beyond the intrasite and intersite correlation terms turns out to be necessary to properly describe the correlated singlet-singlet transitions under pressure.