# ES22 Abstracts

### 2022 Workshop on Recent Developments in Electronic Structure (ES22)

Tuesday, May 31, to Friday, June 3, 2022

at Columbia University

A hybrid workshop with in-person and virtual activities

## Invited Talks

*(in alphabetical order, by speaker's last name)*

**Nongnuch Artrith, Utrecht University**

Title: Modelling of Complex Energy Materials with Machine Learning

Abstract: The properties of materials for energy applications, such as heterogeneous catalysts and battery materials, often depend on complicated chemical compositions and complex structural features including defects and disorder. This complexity makes the direct modelling with first principles methods challenging. Machine-learning (ML) potentials trained on first principles reference data enable linear-scaling atomistic simulations with an accuracy that is close to the reference method at a fraction of the computational cost. ML models can also be trained to predict the outcome of simulations or experiments, bypassing explicit atomistic modelling altogether. Here, I will give an overview of our contributions to the development of ML potentials based on artificial neural networks (ANNs) [1-3] and applications of the method to challenging materials classes including metal and oxide nanoparticles, amorphous phases, and interfaces [4-5]. Further, I will show how large computational and small experimental data sets can be integrated for the ML-guided discovery of catalyst materials [6]. These examples show that the combination of first-principles calculations and ML models is a useful tool for the modelling of nanomaterials and for materials discovery. All data and models are made publicly available. To promote Open Science, we also formulated guidelines for the publication of ML models for chemistry that aim at transparency and reproducibility [7].

References:

1. N. Artrith and A. Urban, Comput. Mater. Sci., 2016, 114, 135.

2. N. Artrith, A. Urban, and G. Ceder, Phys. Rev. B, 2017, 96, 014112.

3. A. Cooper, J. Kästner, A. Urban, and N. Artrith, npj Comput. Mater., 2020, 6, 54.

4. N. Artrith and A.M. Kolpak, Nano Lett., 2014, 14 2670.

5. N. Artrith, J. Phys. Energy, 2019, 1, 032002.

6. N. Artrith, Z. Lin, and J. G. Chen, ACS Catal., 2020, 10, 9438; N. Artrith, Matter 3 (2020) 985–986.

7. N. Artrith, K. Butler, F.X. Coudert, S. Han, O. Isayev, A. Jain, and A. Walsh, Nat. Chem. 13 (2021) 505–508.

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**Dmitri Basov, Columbia University**

Title: Shedding nano-light on quantum materials

Abstract: In this talk, I will describe two recent experiments harnessing nano-scale polaritonic modes (“nano-light”) for probing electronic structure and charge dynamics in van der Waals quantum materials. Specifically, I will discuss massive charge transfer across graphene-αRuCl3 interface [1,2] as well as unconventional electronic properties of the nodal metal ZrSiSe [3].

[1] Daniel J. Rizzo, Bjarke S. Jessen, Zhiyuan Sun, Francesco L. Ruta, Jin Zhang, Jia-Qiang Yan, Lede Xian, Alexander S. McLeod, Michael E. Berkowitz, Kenji Watanabe, Takashi Taniguchi, Stephen E. Nagler, David G. Mandrus, Angel Rubio, Michael M. Fogler, Andrew J. Millis, James C. Hone, Cory R. Dean, and D. N. Basov, “Charge-Transfer Plasmon Polaritons at Graphene/α-RuCl3 Interfaces,” Nano Letters 20, 8438 (2020)

[2] Daniel J. Rizzo, Sara Shabani, Bjarke S. Jessen, Jin Zhang, Alexander S. McLeod, Carmen Rubio-Verdú, Francesco L. Ruta, Matthew Cothrine, Jiaqiang Yan, David G. Mandrus, Stephen E. Nagler, Angel Rubio, James C. Hone, Cory R. Dean, Abhay N. Pasupathy, and D. N. Basov, “Nanometer-Scale Lateral p−n Junctions in Graphene/α-RuCl3 Heterostructures,” Nano Letters 22, 1946 (2022)

[3] Yinming Shao, Aaron J. Sternbach, Brian S. Y. Kim, Andrey A. Rikhter, Xinyi Xu, Umberto De Giovannini, Ran Jing, Sang Hoon Chae, Zhiyuan Sun, Seng Huat Lee, Yanglin Zhu, Zhiqiang Mao, J. Hone, Raquel Queiroz, A. J. Millis, P. James Schuck, A. Rubio, M. M. Fogler, D. N. Basov “Infrared Plasmons Propagate through a Hyperbolic Nodal Metal” (unpublished).

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**Sophie Beck, CCQ-Flatiron Institute**

Title: Realistic materials modeling with charge self-consistency in DFT+DMFT

Abstract: The use of density functional theory (DFT) and dynamical mean field theory (DMFT) has proven successful as a combined approach for electronic structure calculations of strongly correlated materials. While the treatment of local interactions within DMFT was handled for many years as a post-processing correction to the DFT solution (one-shot approach), a more rigorous approach in terms of reaching a thermodynamic stationary point requires an iterative feedback loop between the two methods to allow for an exchange of charge [1]. This means that a solution should be obtained by self-consistency over the charge density, closing the loop in the combined computational approach. In this talk, we will review the impact of the full charge self-consistency on the electronic landscape. We will discuss examples of qualitative and quantitative differences from the one-shot approach and present a recent flexible and open-source implementation based on the Quantum Espresso package for the DFT calculations, the Wannier90 code for the up-/down-folding, and the TRIQS software package for setting up and solving the DMFT equations [2].

References:

[1] F. Lechermann, "Charge self-consistency in correlated electronic structure calculations." DMFT: From Infinite Dimensions to Real Materials, Forschungszentrum Jülich GmbH (2018)

[2] S. Beck, A. Hampel, O. Parcollet, C. Ederer, and A. Georges, J. Phys.: Condens. Matter 34, 235601 (2022)

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**Roberto Car, Princeton University**

Title: Molecular Dynamics with the Deep Potential Method

Abstract: In the last decade, machine learning methods changed substantially the way in which interatomic potentials are constructed from first principles quantum mechanics. In these approaches, deep neural networks, trained on electronic structure data, are used to represent the potential energy surface. Molecular dynamics with machine learned potentials has computational cost and scaling with size comparable to those of empirical force fields, yet it retains much of the accuracy and generality of the adopted ground-state electronic solver. I will focus, in particular, on the deep potential method and its extension to represent the polarization surface, which makes possible studies of the dielectric properties of materials at finite temperature.

I will illustrate the approach with applications to the homogeneous nucleation of ice from the liquid, the ferroelectric phase transition in lead titanate, and the static dielectric constant of liquid water. All these investigations are well beyond the reach of direct first principles molecular dynamics simulations.

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**Yueqing Chang, UIUC **

Title: Minimal effective models from first principles for hydrogen chains in the strongly correlated regime

Abstract: One powerful application of first-principles calculations is to provide effective low-energy descriptions of materials (downfolding). This downfolding is commonly done by assuming a given model, then estimating the model parameters using first-principles results. Examples include computing $J$s using different spin orders, the cRPA-based approaches in which a particular subspace and interaction formulation are chosen, and modifying DFT band structures with interactions. While they can be successful, these approaches are not systematically improvable.

The density matrix downfolding (DMD) approach was proposed [1,2] to resolve this issue. DMD simultaneously accounts for the non-interacting and interacting terms without introducing double counting error. It allows one to systematically improve the downfolded Hamiltonians using more accurate approximations to the Hilbert space, and better parameterizations of the Hamiltonians. In this talk, we apply DMD to hydrogen chains in the strongly correlated regime. Specifically, we show that DMD naturally selects the only relevant parameters in the model for the chosen Hilbert space, with all the parameters renormalized from the bare long-range values. For the hydrogen chains, we show that the minimal effective model on a low-energy Hilbert space spanned by the first few spin-like excitations is a single-band Heisenberg model, where the Heisenberg $J$ stays constant as we increase the system size. The minimal model becomes a single-band Hubbard model when extending the Hilbert space, with $t$ and $U$ depending on the chosen energy cutoff.

References:

[1] H. J. Changlani, H. Zheng, and L. K. Wagner, J. Chem. Phys. 143, 102814 (2015).

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

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**Kun Chen, CCQ-Flatiron Institute **

Title: Picasso’s bull study and the renormalized theory of valence electrons

Abstract: In a search for the real “idea” of a bull, Pablo Picasso created eleven portraits of bulls around 1945. Their outlines gradually become more abstract and minimalistic, going from a detailed lithograph of a real-life bull to a mere outline of its shape. We use a similar idea to analyze several effective models of delocalized valence electrons in materials We discuss the minimalistic renormalized action of the valence electrons and its physical properties.

Other authors: Haule, Kristjan and Kotliar Gabriel from Rutgers University

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**Ismaila Dabo, PennState**

Title: Extensive benchmarking of DFT+U for band-gap predictions and materials discovery

Abstract: Accurate predictions of band gaps are of practical interest to the modeling and development of semiconductor materials, such as photocatalysts and transparent conductors. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band structure predictions beyond that of DFT calculations based on (semi)local functionals[1]. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps [2]. Here, we present a systematic assessment of DFT+U band gaps computed using self-consistent ab-initio U parameters obtained from density-functional perturbation theory to impose the piecewise linearity of the total energy [3]. Applications of DFT+U as a reliable and efficient method for data-intensive materials discovery will also be discussed [4].

References:

[1] Cococcioni M. and de Gironcoli S., Linear response approach to the calculation of the effective interaction parameters in the LDA+ U method, Physical Review B 71, 035105 (2005). DOI: 10.1103/PhysRevB.71.035105

[2] Timrov I., Marzari N. and Cococcioni M., Hubbard parameters from density-functional perturbation theory, Physical Review B 98, 085127 (2018). DOI: 10.1103/PhysRevB.98.085127

[3] Kirchner-Hall N. E., Zhao W., Xiong Y., Timrov I., Dabo I., Extensive benchmarking of DFT+ calculations for predicting band gaps, Applied Sciences 11, 2395 (2021). DOI: 10.3390/app11052395 [

4] Xiong Y., Campbell Q., Fanghanel J., Badding C. K., Wang H., Kirchner-Hall N. E., Theibault M. J., Timrov I., Mondschein J. S., Seth K., Katz R., Molina Villarino A., Pamuk B., Penrod M. E., Khan M. M., Rivera T., Smith N. C., Quintana X., Orbe P., Fennie C. J., Asem-Hiablie S., Young J. L., Deutsch T. G., Cococcioni M., Gopalan V., Abruña H. D., Schaak R. E., Dabo, I., Optimizing accuracy and efficacy in data-driven materials discovery for the solar production of hydrogen, Energy & Environmental Science 14, 2335-2348 (2021). DOI: 10.1039/D0EE02984J

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**Zhenbang Dai, UPenn **

Title: First-principles calculation of ballistic current

Abstract: The bulk photovoltaic effect (BPVE) refers to current generation due to illumination by light in a homogeneous bulk material lacking inversion symmetry. In addition to the intensively studied shift current, the ballistic current, which originates from asymmetric carrier generation due to scattering processes, also constitutes an important contribution to the overall kinetic model of the BPVE. In this talk, I will introduce our recent work where we attempted to calculate the ballistic current from two intrinsic contributions: electron-phonon (e-ph) scattering and electron-hole (e-h) scattering. Using a perturbative approach, we derived formulae for the two mechanisms in a form amenable to first-principles calculation, and a different approach based on Bethe-Salpeter Equation (BSE) for electron-hole mechanism will also be developed. In addition, I will discuss the difficulties when evaluating these formulae numerically and the ways of overcoming them. With the help of quantum-mechanical density functional theory and GW theory, we then implemented the theory and calculate the ballistic current of two materials, the prototypical BPVE material BaTiO3 and a 2D material monolayer MoS2. The magnitude of the e-ph mechanism ballistic current is comparable to that of the shift current, and the total spectrum (shift plus ballistic) agrees well with the experimentally measured photocurrents. However, for e-h contribution, both methods have shown it to be less appreciable than other mechanisms, so it could thus be safely neglected when analyzing the experimental BPVE photocurrents. Not only has our work significantly advanced the fundamental understanding of BPVE, but the first-principles approaches provided here will be also beneficial for material prediction and design in order to search for materials with a larger ballistic current.

References:

[1] Z. Dai, A. M. Schankler, L. Gao, L. Z. Tan and A. M. Rappe. Phonon-Assisted Ballistic Current from First-Principles Calculations. Physical review letters, 126(17), 177403 (2021).

[2] Z. Dai and A. M. Rappe, First-principles calculation of ballistic current from electron-hole interaction. Physical Review B, 104(23), 235203 (2021)

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**Marivi Fernandez-Serra, Stony Brook University**

Title: Highly accurate and constrained density functional obtained with differentiable programming

Finding the true exchange and correlation (XC) functional would render DFT exact. However, the true form of this elusive functional is so far unknown, and there is little hope that it can ever be written down in a closed-form expression. For practical applications, it has to be approximated. Many approximations, varying in complexity and accuracy, exist, and researchers have to decide on a case-by-case basis which functional to use. Doing so, however, is far from ideal, as the added degree of freedom can introduce hard-to-control systematic errors. I will outline avenues for creating new XC functionals with the help of neural networks, a machine learning method. Neural networks are considered universal approximators, which means they can fit any function with arbitrary accuracy. For this reason, some people believe machine learning might hold the key to achieving something close to an exact functional. We introduce the concept of physically informed machine learning and propose two approaches to fitting density functionals. In one approach, prior physical knowledge is injected into the training procedure by learning to add small corrections to physically motivated calculations. Our second approach demonstrates how physical information can be directly incorporated into the optimization algorithm in the form of differential equations. We show that both approaches lead to machine learning models that are significantly more data-efficient and reliable than those without physical priors. Trained automatically, the thus created models routinely outperform carefully hand-designed functionals. However, we also find that caution needs to be exercised when using machine-learned models, as they lack some of the safety-nets that traditional functionals are designed with and therefore run the risk of failing in unexpected scenarios.

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**Claudia Filippi, University of Twente**

Title: Excited-state calculations with quantum Monte Carlo

Abstract: While quantum Monte Carlo methods are routinely employed to predict accurate ground-state energies of relatively large systems, their use is relatively uncommon when coming to excited states, especially for properties other than total energies. Here, we will illustrate their performance in combination with different choices of Jastrow-Slater wave functions, when variational and structural parameters are consistently optimized within the method. For several challenging, increasingly large molecules, we will show that the use of a selected-configuration-interaction scheme to generate compact determinantal components leads to the fast and accurate computation of ground- and excited-state structures as well as excitation energies of different nature, already at the variational Monte Carlo level. Finally, we will discuss the use of different variational principles in quantum Monte Carlo to target the states involved in the excitation.

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**Feliciano Giustino, UT-Austin **

Title: Phonon-driven Rashba-Dresselhaus effect

Martin Schlipf (1), Feliciano Giustino (2)

1) VASP Software GmbH

2) The University of Texas at Austin

The Rashba-Dresselhaus effect is the splitting of doubly degenerate band extrema in semiconductors, accompanied by the emergence of counter-rotating spin textures and spin-momentum locking. In this talk we will discuss some recent work on the relation between lattice vibrations in solids and the Rashba-Dresselhaus effect. At an intuitive level, vibrations break inversion symmetry and therefore should lead to band splitting and spin reorientation. A natural question that emerges is under which conditions phonons and the electron-phonon interactions can induce a dynamic Rashba-Dresselhaus effect. To answer this question, we performed a detailed analysis of the energy splitting using a many-body approach. We found that, in non-magnetic crystals with an inversion center, an equilibrium phonon population does not induce band splitting to any order of perturbation theory. Conversely, a non-equilibrium phonon population can lead to sizable band splitting. In particular, we show that by coherently exciting long-walenength infrared-active phonons it should be possible to establish spin textures with Rashba, Dresselhaus, or Weyl patterns depending on the symmetry of the vibrational eigenmodes. We discuss the experimental feasibility of this proposal by considering the photoluminescence of light-driven lead halide perovskites.

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**Sinead Griffin, Lawrence Berkeley Laboratory**

Title: Nonequilibrium Topological Materials in Space and Time

The topological classification of materials has so far been intimately connected to the presence of translational symmetries in crystalline materials at equilibrium. However, recent experiments have hinted at the presence of topologically protected states even in the absence of translational symmetry, and in non-equilibrium, transiently-induced phases. In this talk I will discuss how theoretical calculations have uncovered topological phases in such nonequilibrium systems, and suggest general routes for achieving them in real materials. I will illustrate this by first describing how introducing structural disorder into the BiTeI layered family of Rashba materials can induce a trivial-to-nontrivial topological phase transition. I will then extend this to the amorphous limit where theory and ARPES measurements suggest topologically protected surface states in amorphous Bi2Se3. Finally, I will discuss how transiently-induced topological phase transitions can be achieved through selective phonon probing, and how their lifetime can be extended through nonlinear phononic couplings.

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**Sohrab Ismail-Beigi, Yale University**

Title: Slave-boson approach for localized electronic interactions: methods and software

Abstract: For materials featuring strong electron-electron interactions, e.g., many transition metal oxides (TMOs), aspects of the low-energy electronic structure are difficult to capture by using standard band theory approaches such as density-functional theory (DFT) and its variants. These include dynamical renormalization of electronic masses, transfer of spectral weight away from low-energy quasiparticle states, and formation of Hubbard bands (especially without any symmetry breaking). These are dynamical electronic structure effects that cannot be described by band theory approaches (e.g., DFT, DFT+U or hybrid methods). Describing such effects in a computationally efficient and accurate manner is an ongoing challenge for the field of electronic structure theory.

We describe a class of slave-boson methods which provide efficient, albeit approximate, solutions for the low-energy states of extended Hubbard models that describe the electronic states in TMOs. We begin with a pedagogical overview of the philosophy of these slave-boson methods. We then describe the standard “single-site” approximation (i.e., an interacting site coupled to a self-consistent bath) [1-3], our open software implementation of this approach [3-4], and some comparisons to experiments and dynamical mean field theory. We end by highlighting our recent improvements in methodology that move beyond the single-site approximation by solving clusters of interacting sites.

[1] Georgescu and Ismail-Beigi, PRB 92, 235117 (2015)

[2] Georgescu and Ismail-Beigi, PRB 96, 165135 (2017)

[3] Georgescu, Kim and Ismail-Beigi, Comp. Phys. Comm. 265, 107991 (2021)

[4] bitbucket.org/yalebosscode/boss

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**Felipe H. da Jornada, Stanford University**

Title: Excited states in atomically thin moiré materials and their dynamics

bstract The synthesis of quasi-two-dimensional materials, such as monolayer transition metal dichalcogenides (TMDCs), has opened the door to the study of new classes of systems with nanoscale dimensionality confinement and weak electronic screening, leading to strongly enhanced electron interactions. Heterobilayers of such materials, in particular, host unique physics due to the emergence of a moiré potential that modulates such excitations. However, the interplay between the structural details in such twisted bilayer structures (including atomistic relaxation effects), is poorly understood, and often relies on empirically fitted continuum models. In this talk, we present results obtained from recent formalisms and methods we developed to bridge these effects and phenomena. We show how moiré effects can lead to a surprising localization of excitons even for relatively large twist angles (~2°) – associated with a moiré lattice parameter of ~ 6 nm. We also show a new *ab initio* framework to compute exciton- phonon coupling and the linewidth associated with discrete excitonic states based on many-body perturbation theory. Our approach predicts a linewidth up to 3x larger than that obtained from a Fermi’s-golden rule approach based on a relaxation time approximation, in good agreement with experiment.

Funding: This work was supported by the Center for Computational Study of Excited-State Phenomena in Energy Materials (C2SEPEM) at LBNL, funded by the U.S. DOE under Contract No. DE-AC02- 05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231.

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**Joonho Lee, Columbia University and Google Quantum AI**

Title: A Good Use of Quantum Computers in Quantum Monte Carlo Simulations of Molecules and Solids

Abstract: Due to the fermionic sign problem, it is generally necessary to impose approximate boundary conditions on imaginary time propagation in quantum Monte Carlo (QMC). These approximations then introduce an error in the final ground state energy, which is wholly determined by the quality of trial wavefunctions. We will present a quantum-classical hybrid algorithm, called QC-QMC [1], which is an attempt to reduce the error in QMC by utilizing more sophisticated trial wavefunctions that are intractable to use on classical computers. This idea has been implemented on Google’s Sycamore processor and demonstrated accuracy competitive with state-of-the-art quantum chemistry methods up to 16-qubit and 120 orbitals total. While this is currently the largest quantum computation of chemical problems to date, we will note challenges towards realizing one of the first practical quantum advantages.

[1] Huggins et al., Nature, 603, 416–420 (2022)

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**Susi Lehtola, Molecular Science Software Institute**

Title: On the reproducibility of density functional approximations

Abstract: Density functional theory is the workhorse of modern-day chemistry and materials science, and several novel density functional approximations (DFAs) are published every year. In order for the novel DFAs to become available for users of various program packages, they need to be implemented in the used programs. However, a constant problem with re-implementing DFAs reported in the literature is the lack of reliable, or sufficiently accurate, reference data. The lack of a common standard to test new implementations against has lead to some non-equivalent implementations of commonly-used functionals such as BP86, PW91, PBE, as well as B3LYP across various program packages, as we demonstrate in this work. The small differences in parameter values can result in noticeable discrepancies in total energies in fully numerical calculations targeting \mu E_{h} precision. Our reimplementations of several more recently published functionals have also revealed many issues with incorrect functional forms that were only discovered through careful numerical benchmarks. When consistent choices are made for the numerical parameters in the DFA, and the total energy is evaluated to high accuracy, achieving sub-\mu E_{h} agreement between Gaussian basis set calculations carried out in different programs is routinely achievable.

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**Kai-Hsin Liou, UT-Austin**

Title: Real-space methods for large electronic structure calculations

Abstract: First-principles electronic structure calculations are a popular tool for understanding and predicting properties of materials. Among such methods, the combination of real-space density functional theory and pseudopotentials to solve the Kohn-Sham equations has several advantages. Real-space formalisms, such as finite differences and finite elements, avoid the global communication needed in fast Fourier transformation and offer better scalability for large calculations on hundreds or thousands of compute nodes. Besides, finite-difference methods with a uniform real-space grid are easy to implement, e.g., the convergence of a Kohn-Sham solution is controlled by a single parameter – the grid spacing.

One promising algorithm for solving the Kohn-Sham eigenvalue problem in real space is the Chebyshev-filtered subspace iteration method (CheFSI). Within this algorithm, the charge density is constructed without regard to a solution for individual eigenvalues. However, for large systems CheFSI may suffer from super-linear scaling operations such as orthonormalization and employing the Rayleigh–Ritz method.

I will illustrate two improvements on CheFSI to enhance scalability and accelerate the calculations. The first one is a hybrid method that combines a spectrum slicing method and CheFSI. The spectrum slicing method divides a Kohn–Sham eigenvalue problem into subproblems, wherein each subproblem can be solved in parallel using CheFSI. We will show that, by the simulations of confined systems with thousands of atoms, this hybrid method can be faster and possesses better scalability than CheFSI. The second improvement is a grid partitioning method based on space-filling curves (SFC). SFC improves the efficiency of the sparse matrix–vector multiplication, which is the key component in CheFSI. We will show, by computations of confined systems with 50,000 atoms or 200,000 electrons, that this method effectively reduces the communication overhead and improves the utilization of the vector processing capabilities provided by most modern parallel computers.

Other Authors: Yang, Chao (Lawrence Berkeley National Laboratory) Biller, Ariel (Weizmann Institute of Science) Kronik, Leeor (Weizmann Institute of Science) Chelikowsky, James R. (University of Texas at Austin)

References:

[1] Kai-Hsin Liou, Chao Yang, James R. Chelikowsky, “Scalable Implementation of Polynomial Filtering for Density Functional Theory Calculation in PARSEC,” Computer Physics Communications 254, 107330 (2020).

[2] Kai-Hsin Liou, Ariel Biller, Leeor Kronik, James R. Chelikowsky, “Space-Filling Curves for Real-Space Electronic Structure Calculations,” Journal of Chemical Theory and Computation 17, 4039-4048 (2021).

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**Chris Marianetti, Columbia University**

Title: Precise ground state of multi-orbital Mott systems via the variational discrete action theory

Abstract: Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to simultaneously reach zero temperature and infinite system size. Even in infinite dimensions, the solution via the dynamical mean-field theory (DMFT) is limited by the absence of unbiased impurity solvers for zero temperature and multiple orbitals. The recently developed variational discrete action theory (VDAT) offers a new approach, with a variational ansatz that is controlled by an integer N, and monotonically approaches the exact solution at an exponentially increasing computational cost. Here we implement VDAT for the multi-orbital Hubbard model in d=infinity for N=2-4. At N=2, VDAT rigorously recovers the multi-orbital Gutzwiller approximation, reproducing known results. At N=3, VDAT qualitatively and quantitatively captures the competition between U, J, and the crystal field in the two band Hubbard model, with a negligible computational cost. VDAT will have far ranging implications for understanding strongly correlated materials.

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**Miguel Morales, CCQ-Flatiron Institute**

Title: Auxiliary field quantum Monte Carlo of Solids

Abstract: I will present an overview of the recent efforts to extend the applicability of the Auxiliary-Field quantum Monte Carlo method to realistic materials, with the goal of developing a highly predictive, parameter- free, robust and flexible computational tool for the study of correlated solids. I will focus on recent developments aimed at reducing the severity of many of the challenges presented by the extension of the method to realistic solids. Some of these developments include: i) compact representations of the second- quantized Hamiltonian, ii) efficient GPU implementations, iii) optimized correlation-consistent basis sets for solids, and iv) systematically improvable trial wave-functions. The AFQMC method is very well suited for emerging GPU architectures, obtaining large performance gains compared to CPU implementations. These performance gains translate in a significant extension in recent years in the applicability and utility of the method, making it a valuable tool in the study of materials from first principles.

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**Steve Ndengue, University of Rwanda**

Title: Wavepacket studies of the water-dimer: New insights from 12D quantum dynamics

Abstract: Water is of fundamental importance in every aspect of daily life. As a result, a lot of effort has been devoted in understanding its properties. It is understood in the community that the study of water complexes and clusters provides an understanding of the important features of the condensed phases. The study of 2, 3 and more bodies interaction also provide an estimate of the importance of these interactions in liquid water. The water-dimer (H2O-H2O) which is the simplest water cluster has been widely studied even up to a recent past, both theoretically and experimentally. While the intermolecular interaction and vibrational signatures for the cluster have been very accurately described, a less definite characterization of the infrared spectrum stretch region still remains. In the past couple of years, two seperate works were published and brought back some issues related to the assignment of structures observed on the low temperature infrared spectrum of the dimer. With the help of accurate wavepacket (MCTDH) quantum dynamics simulations on a recent 12D Potential Energy and Dipole Moment Surfaces obtained at the CCSD(T) level of theory, we revisit the water-dimer infrared spectrum in the OH-stretch region and establish the vibrational origin of all the structures observed experimentally. The results highlight the contribution of the degenerate ground vibrational states on the spectroscopic signatures and validate prior theoretical description of the system.

Other authors: Schroder, Markus & Institute of Physical Chemistry, University of Heidelberg and Meyer, Hans-Dieter & Institute of Physical Chemistry, University of Heidelberg and Vendrell, Oriol & Institute of Physical Chemistry, University of Heidelberg and Zhang, Zhaojun & Dalian Institute of Chemical Physics, Chinese Academy of Sciences and Zhang, Dong Hui & Dalian Institute of Chemical Physics, Chinese Academy of Sciences and Gatti, Fabien & Institut de Sciences Moleculaires d'Orsay, CNRS - University Paris-Saclay

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**Talat Rahman, University of Central Florida**

Title: Time-dependent properties of strongly correlated materials: building and applying an ab initio tool

Abstract: Accurate description of the temporal evolution of strongly correlated materials, when perturbed by an external field, is a challenging and interesting problem in condensed matter physics and material science. This is particularly the case for the ultrafast (femtosecond) response of the system which may be dominated by electron correlations, unhindered by interactions, for example with the lattice. At the computational level, time-dependent density-functional theory (TDDFT) when equipped with appropriate exchange-correlation (XC) functional offers a way forward. This necessarily implies going beyond the standard local density or the generalized gradient approximations because of the inability to treat on-site orbital-resolved correlations and/or time dependent interactions. In this presentation, we provide details of our new methodology in which we combine dynamical mean-field theory and TDDFT (DMFT-TDDFT) to examine the ultrafast response of materials with strong electron-electron correlations. We obtain a non-adiabatic XC kernel (potential for the nonlinear case) from the electron charge susceptibility (self-energy) by solving an effective Hubbard model using DMFT. This XC kernel or potential when implemented in TDDFT is suitable for examination of nonequilibrium properties of systems. We demonstrate the viability of the approach through computation of the ultrafast demagnetization of Ni [1], for which we calculate the pre-thermalization of the electron and hole subsystems and related spin-resolved properties. We demonstrate that the system magnetic moment reaches its lower, transient-state value (demagnetization) in tens of femtoseconds, and that the charge (electron and hole) pre-thermalization occurs ~10 femtoseconds, both results in agreement with experimental data. Since at such short time scales electron-electron interaction is the only source of scattering in the system, these results capture the power of the methodology for isolating the femtosecond physics of strongly correlated materials.

This work was supported in part by DOE grant DE-FG02-07ER46354.

[1] S. R. Acharya, V. Turkowski, G-p Zhang, and T. S. Rahman, Phys. Rev. Lett. 125, 017202 (2020). https://doi.org/10.1103/PhysRevLett.125.017202

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**Kyle Sherbert, University of North Texas **

Title: Band theory on a quantum computer

Abstract: Quantum computers promise to revolutionize our capability to simulate molecules and materials, but their utility in cutting-edge research is still a little ways off. In the meantime, it is helpful (and fun!) to understand how to best use quantum computers on problems we already know the answer to. Therefore, I will illustrate exactly how to apply the popular Variational Quantum Eigensolver (VQE) to solve the electronic band structure of a periodic system, as approached from a few different angles. My talk will demonstrate the thought behind qubit mapping, operator estimation, and quantum circuit design – three fundamental aspects of any quantum algorithm for quantum chemistry.

Authors: Sherbert, Kyle (University of North Texas) and Buongiorno Nardelli, Marco (University of North Texas, Santa Fe Institute)

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**Max Stengel, Institut de Ciència de Materials de Barcelona**

Title: Flexoelectricity and long-range Coulomb interactions: from 3D to 2D

Abstract: Flexoelectricity, describing the polarization response to a gradient of the strain, is a universal property of all insulators that has attracted considerable attention in the past few years. In spite of its fundamental and practical interest, it has long resisted theoretical attempts at quantifying it with predictive accuracy in realistic materials. In this talk, I will review the methodological advances that have recently lifted this limitation in the context of first-principles electronic-structure theory. The main idea consists in combining the long-wavelength method, a workhorse of condensed-matter theorists since the early days of Born and Huang, with modern density-functional perturbation theory. This allows one to calculate not only flexoelectricity but, in full generality, the response to spatial gradients of an arbitrary field. As an illustrative example, I will discuss the dynamical quadrupole tensor, and its importance for the accurate description of interatomic forces and electron-phonon couplings. I will also emphasize the formal differences between the three-dimensional and two-dimensional cases.

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**Yang Sun, Iowa State University **

Title: Simulations of iron in the Earth’s core conditions

Abstract: Iron is the primary element in the Earth’s core. The properties of iron under extremely high PT conditions are fundamental to understanding the Earth’s internal structure and evolution. Ab initio simulations provide important iron information that is hard to access from laboratory or seismic data. In this talk, I will show our recent work using DFT calculations coupled with molecular dynamics and genetic algorithm/Monte-Car simulations to understand the formation of the Earth’s inner core and to discover iron-rich FeO compounds possibly existing in the inner core. First, I will discuss the nucleation process of the Earth’s inner core. Recent attempts to explain how the inner core solidified were surprisingly unsuccessful, which led to the so-called “inner core nucleation paradox”. To address the paradox, we developed potentials from ab initio data to simulate the iron’s crystallization process under core’s conditions. We demonstrate molten iron could crystallize into the hcp phase via a two-step nucleation process with an intermediate bcc phase under the Earth's core conditions [1,2]. This provides a key factor in understanding the initial formation of the inner core and its present crystal structures. Next, I will show how we identify iron-rich Fe-O compounds and use it to solve the complex XRD data from high PT experiments. It has been thought only oxygen-rich Fe-O compounds exist. Using crystal structure prediction and DFT calculations, we discovered a new family of iron-rich FeO compounds at Earth’s core conditions. This challenges the traditional view and suggests that oxygen should be a possible light element in the solid inner core. The existence of these oxygen-bearing phases could extend the deep oxygen cycling to the solid inner core, an entirely global oxygen cycle [3].

References:

[1] Y. Sun, F. Zhang, Mikhail I. Mendelev, R. M. Wentzcovitch, and K.-M. Ho, "Two-step nucleation of the Earth's inner core", Proc. Natl. Acad. Sci. U.S.A. 119, e2113059119 (2022)

[2] Y. Sun, M. I. Mendelev, F. Zhang, X. Liu, B. Da, C.-Z. Wang, R. M. Wentzcovitch, K.-M. Ho, "Ab initio melting temperatures of bcc and hcp iron under the Earth's inner core condition", arXiv:2205.02290 (2022)

[3] J. Liu, Y. Sun, C. Lv, F. Zhang, S. Fu, V. B. Prakapenka, C.-Z. Wang, K.-M. Ho, J.-F. Lin, R. M. Wentzcovitch, “Iron-rich Fe-O compounds with closest-packed layers at core pressures”, arXiv:2110.00524 (2021)

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**Vojtěch Vlček, UC Santa Barbara **

Title: Dynamical electronic correlations: from models to materials

Abstract: I will discuss the role of dynamical correlations in predicting electronic excitation spectra in systems ranging from molecules to condensed systems with thousands of electrons. Using the many-body perturbation theory based on Green's function formalism, we can study individual quasiparticle states and even non-trivial quasiparticle-quasiparticle interactions. First, I will exemplify these approaches on small test systems, for which we can find numerically exact excitation spectra and study the role of various theoretical formulations. Second, I will show practical applications to quantum materials, e.g., in studying the correlated phenomena for localized moire states in twisted bilayer graphene. For the latter, we employ our real-space and real-time stochastic methods and combine them with embedding and ab-initio downfolding onto explicitly correlated Hamiltonians. This framework, leveraging efficient low-scaling numerical techniques, is generally applicable to (quantum) material science and chemistry problems and constitutes an ideal platform for simulating complex nanoscale systems with thousands of electrons at a minimal computational cost.

## Poster Session Abstracts

The poster session will take place from 7:00-10:00 PM on Tuesday, June 1, 2022.

#### ES22 Workshop Information

Please see this page for more information about the workshop.