Session A60: Quantum Embedding: Materials and Methods for Materials

Invited Talk: Jernej MravljeSpectroscopies of Hund's metals within (DFT+)DMFT: electronic Raman response in Sr2RuO4

Spectrocopically, Hund's metals (e.g. ruthenates, iron-based superconductors) are characterized by multiplet splittings of the Hubbard bands and a particular shape of the quasiparticle peak associated to a two-stage screening of the spin and orbital momentums. We recently found another feature, stemming from strong charge fluctuations in Hund's metals, which leads to a side-peak at energy given exclusively by the value of Hund's rule coupling, that I will discuss based on dynamical mean-field theory results for a three orbital model Hund's metal. I will discuss the appearance of those features in photoemission and optical spectroscopies.

Another characteristics of Hund's metals in general and of the normal state of the unconventional superconductor Sr₂RuO₄ in particular is the strong orbital differentiation. Raman scattering allows in principle to access the response associated to different orbitals by coupling to light in different polarization channels.  We calculate electronic Raman response of Sr₂RuO₄ using a combination of density-functional theory and dynamical mean-field theory methods. We calculated the Raman vertex tensors within the effective mass approximation. We found considerably different response in the B_1g and B_2g channels, with less coherent response found in the B_2g channel that is nominally sensitive to the more correlated xy orbital (and associated γ Fermi surface sheet), consistent with measurements of Philippe et al., Phys. Rev. B 103, 235147 (2021). However, precise investigation of different contributions to the response points to important interband couplings enhanced by the finite-frequency nesting between γ and β Fermi surface sheets, which strongly influence the response in the B2g channel. Our results indicate the importance of realistic first-principle based approaches in the interpretation of electronic Raman spectroscopies.

    

Magnetic Properties and Pseudogap Formation in Infinite-Layer Nickelates: Insights From the Single-Band Hubbard Model

We study the magnetic and spectral properties of a single-band Hubbard model for the infinite-layer nickelate compound LaNiO₂. As spatial correlations turn out to be the key ingredient for understanding its physics, we use two complementary extensions of the dynamical mean-field theory to take them into account: the cellular dynamical mean-field theory and the dynamical vertex approximation. Additionally to the systematic analysis of the doping dependence of the non-Curie-Weiss behavior of the uniform magnetic susceptibility, we provide insight into its relation to the formation of a pseudogap regime by the calculation of the one-particle spectral function and the magnetic correlation length. The latter is of the order of a few lattice spacings when the pseudogap opens, indicating a strong-coupling pseudogap formation in analogy to cuprates.   

Moire Materials as laboratories for quantum embedding theories

Quantum embedding theories such as dynamical mean field theory approximate the full quantum dynamics and thermodynamics of an interacting electron system in terms of the properties of a ``quantum impurity model” (few degree of freedom quantum system coupled to non or weakly-interacting bath). The downfolding of the full interacting system to the impurity model, and the adequacy of the quantum impurity model are important open issues in the theory of correlated quantum materials. ``Moire” materials comprised of two or more atomically thin sheets with a lattice constant mismatch or a relative twist angle have emerged as an important experimental platform for the investigation of correlated electron physics, due to the exceptional tunability of unit cell size and symmetry, electron concentration, interaction strength and other properties and to the ability to access parameter regimes inaccessible in conventional solids.   This talk will summarize recent applications of embedding theories to experiments on Moire materials, including tests of the dynamical mean field picture of the metal insulator transition in the presence of Zeeman and orbital coupling to magnetic fields, the theory of transport near van Hove singularities and at high temperatures, and orbital-selective Mott and heavy fermion physics.

This work is based on collaborations with Jiawei Zang, Jennifer Cano, Antoine Georges, Armelle Celarier, Chris Marianetti, Zhengqian Cheng, Daniele Guerci, Valentin Crepel, Thomas Schaefer and Marcel Klett.    

Green's function formulation of quantum defect embedding theory

We present a Green’s function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the G₀W₀ approximation [1]. We show the robustness of our methodology by applying the theory with the newly derived double counting scheme to several defects in diamond. We discuss a strategy to obtain converged results as a function of the size and composition of the active space. The results show that QDET, as implemented in the WEST code (http://west-code.org), is a promising approach to investigate strongly correlated states of defects in solids. Finally, we discuss how to carry-out QDET calculations on GPUs [2] and noisy intermediate-scale quantum computers [3]. 

[1] N. Sheng, C. Vorwerk, M. Govoni, G. Galli, J. Chem. Theory Comput. 18, 3512 (2022).

[2] V. Yu, M. Govoni, J. Chem. Theory Comput. 18, 4690 (2022).

[3] B. Huang, M. Govoni, G. Galli, PRX Quantum 3, 010339 (2022).   

Comparing ab-initio diffusion Monte Carlo and quantum embedding excited state calculations for an Fe3+ point defect in AlN

Quantitative predictions of point defect excited states aid in materials design for optoelectronics and quantum information. However, certain defect excited states – such as those of substitutional Fe_Al³⁺-in-AlN – require multi-determinant wave functions [1]. Ab-initio quantum embedding (QE) calculations balance accuracy and scalability by treating a small active space with an interacting theory. However, prior QE results for Fe³⁺-in-AlN showed qualitative dependence on double counting and functional approximations [2], so higher-accuracy reference calculations are needed.

 

Diffusion Monte Carlo (DMC) calculations have achieved high accuracy even for large, periodic systems using correlated, compact trial wave functions [3]. DMC excited state calculations are now possible by penalizing wave function overlaps during optimization [4]. We establish DMC’s accuracy and QE’s errors on the low-lying excited states of Fe³⁺-in-AlN by comparing their spectra against each other and experiment.

 

[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).

[4] S. Pathak, et. al., J. Chem. Phys. 154 034101 (2021).   

State-specific Variational Quantum Monte Carlo for Point Defect Excited States

In recent years, much progress has been made in electronic structure calculations of spin defects from first principles, for example using quantum embedding theories [1,2]. However, several important controversies remain open in comparing different theoretical approaches and their respective results with experiments. Hence, the development of methods to obtain systematically improvable reference excitation energies of defects is a key priority. Quantum Monte Carlo techniques, particularly state-specific Variational Monte Carlo, have recently seen significant progress in the quality of the wave function ansatzes and optimization algorithms that can be employed for the description of excited states and have provided reliable excitation energies in molecular settings [3]. In this work, we extend the use of state-specific Variational Monte Carlo to the investigation of excited states of point defects in solids with the QMCPACK code and present preliminary results characterizing its accuracy, with the vacancy defect in diamond as an initial test case.

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

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

[3] L. Otis, I. Craig, and E. Neuscamman. J. Chem. Phys. 153, 234105 (2020).

    

Low-energy effective models for 2D hydrogen square lattices derived from first principles

Effective model Hamiltonians use a small set of interactions to represent the physics of strongly correlated systems. To accurately represent real materials, effective models can be downfolded from first-principles calculations; however, using current methods, it can be difficult to assess systematic errors of the resulting models. The density matrix downfolding (DMD) procedure addresses this challenge by allowing the use of standard statistical analysis tools to quantify the errors of effective models fit to first-principles data [1].

We have applied DMD to a computationally simple strongly correlated material, a 2D finite square lattice of hydrogen. The energy spectra of the resulting tight-binding and Hubbard effective models were compared against first-principles data. Our results show that for 2D square hydrogen, the addition of the on-site electron interaction term U greatly improves the fit of the effective model.

[1] H. Zheng et. al., Front. Phys. 6, 43 (2018).   

Functional theory of the spectral density via local embedding

We address the problem of interacting electrons in an external potential by introducing the local spectral density as fundamental variable. First we formulate the problem using an embedding framework and prove a one-to-one correspondence between a spectral density and the local, dynamical external potential playing the role of embedding self-energy. Then, we use the Klein functional to (i) define a universal functional of the spectral density, (ii) introduce a variational principle for the total energy, and (iii) formulate a non-interacting mapping suitable for numerical applications.

We adopt a sum-over-poles representation for the propagators combined with a recently introduced algorithmic inversion method which allow us to efficiently solve the Dyson equations (involving dynamical potentials) arising from the above formulation.

At variance with time-dependent density-functional theory, this formulation aims at studying charged excitations with a functional theory, and, given the more informative content of the spectral density, can also lead to more accurate approximations for the total energy.   

AutoBZ.jl: An Open-Source Library for Automatic and Adaptive Brillouin Zone Integration

Brillouin zone integration is a standard operation in electronic structure calculations used to compute a wide range of physical observables. For systems at finite temperature with a significant scattering rate, represented by a large broadening factor $eta$, standard equispaced integration methods are highly effective. However, when the broadening $eta$ is small, adaptive methods become necessary to achieve converged results. The AutoBZ.jl library introduces both generic and specialized integration routines implementing automatic, optimized, and high-order accurate methods for integrals, with both large and small broadening, using Wannier interpolation. The package automatically selects the suitable integration routine for a given system and is optimized to use the irreducible Brillouin zone based on crystal symmetries. Written in Julia, the library is both extensible and performant, interfaces with Python, and obtains the ab-initio Hamiltonian as standard output of Wannier90. Code examples are demonstrated using calculations of the density of states and optical conductivity of the correlated metal SrVO$_3$ with broadening down to the sub-meV scale.   

Quantum Embedding Methods to investigate oxygen vacancies in Bulk MgO

Quantum embedding methods enable treating different parts of a system at distinct levels of electronic structure theory. For instance, the strongly correlated states of defects in solids may be treated at a higher level of theory than the rest of the system. Quantum defect embedding theory (QDET) [1,2] and periodic density matrix embedding theory (pDMET) [3] are two different methods, the former based on Green’s function embedding, and the latter using the Schmidt decomposition of the system’s density matrix. In this work we employ QDET (and the WEST code) and pDMET (and the PySCF code) to investigate the F⁰ center (neutral oxygen vacancy) in bulk MgO, which gives rise to a singly occupied localized defect state within the solid band gap. We investigate the orbital character of the defect state and compare the extrapolated vertical excitation energies obtained from the two embedding techniques. The active spaces derived from QDET and DMET are in good agreement with each other, however some of the computed excitation energies between multi-reference states differ. Work is in progress to analyze in detail the impact of all the approximations involved in QDET and DMET on the computed vertical excitation energies and compare them with experiments.