Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session P18: Electronic Structure Methods and Quantum Many-body Systems |
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Sponsoring Units: DCOMP DMP Chair: Lubos Mitas, North Carolina State Univ Room: LACC 306B |
Wednesday, March 7, 2018 2:30PM - 2:42PM |
P18.00001: Low-Scaling MP2 for Solids Tobias Schaefer, Georg Kresse Hartree-Fock plus Second-order Møller-Plesset perturbation theory (HF+MP2) is a standard approach in materials physics and quantum chemistry to evaluate the energy of matter. However, this is computationally very demanding since conventional MP2 implementations scale with the fifth power of the system size, Ο(N^{5}), and are difficult to parallelize. We present two low-complexity implementations that have a lower scaling and an almost ideal parallelization efficiency. The key concept of both approaches is to eliminate the summation over all combinations of occupied and unoccupied states, which can be elegantly achieved in the Laplace transformed MP2 formulation. In this way we attain a quartic scaling high performance algorithm, Ο(N^{4}), in the plane-wave basis without introducing further approximations. Moreover, using stochastic HF orbitals, a cubic scaling, Ο(N^{3}), can be achieved when a fixed absolute error is assumed which turns into a linear scaling, Ο(N^{1}), when only a fixed relative error is assumed (e.g. per atom). Analogously, the approaches could allow us to calculate second-order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. |
Wednesday, March 7, 2018 2:42PM - 2:54PM |
P18.00002: Independent Operators for Interacting Electrons Roger Haydock Operators which add an electron to an interacting system and satisfy the time-independent Heisenberg equation are independent in the sense that they are completely decoupled from one another. The energies of these operators describe the electronic structure of the system and can be used to determine energies of interacting many electron states. This is illustrated with a calculation of the gap in a Hubbard model for a cubic crystal of s-electrons. |
Wednesday, March 7, 2018 2:54PM - 3:06PM |
P18.00003: On the question of the total energy in FLO-SIC calculations Kushantha Withanage, Kai Trepte, Koblar Jackson, Juan Peralta The Fermi-Löwdin orbital self-interaction correction (FLO-SIC) formalism is a promising approach for treating the self-interaction error in density functional theory (DFT)^{1,2,3,4}. Minimizing the total energy in FLO-SIC requires finding optimal positions for the Fermi orbital descriptors. Hence only 3N parameters are involved. Previous SIC calculations satisfied constraints known as the localization equations (LEs), involving the variation of N(N-1)/2 parameters. This raises the question of whether FLO-SIC reaches the same total energy as obtained in SIC-LE calculations. To address this, we implemented a method to perform SIC-LE calculations within the same NRLMOL code that is used for FLO-SIC calculations. Here we compare total energies of a diverse set of atoms and molecules, as well as the molecular atomization energies from fully self-consistent FLO-SIC and SIC-LE calculations. |
Wednesday, March 7, 2018 3:06PM - 3:18PM |
P18.00004: Localized and Randomized Algorithms for Electronic Structure Jonathan Moussa, Andrew Baczewski The computational cost of conventional electronic structure algorithms is cubic-scaling in system size. Quadratic scaling is possible with polynomial or rational approximation of the Fermi-Dirac function applied to the electronic Hamiltonian, but such algorithms are only beneficial for large system sizes. Further reduction to linear scaling is possible by using localization [Rev. Mod. Phys. 71, 1085 (1999)] or randomization [Phys. Rev. Lett. 111, 106402 (2013)], but localized algorithms perform poorly for low-temperature metals and randomized algorithms perform poorly for small error tolerances. We combine localized and randomized algorithms to offset their individual weaknesses – we reduce variance by randomly sampling from a residual error in a localized density matrix approximation rather than the full density matrix and reduce the cost per sample by using localized Green’s functions to precondition the evaluation of rational approximations. We compare this methods with quadratic-scaling PEXSI and cubic-scaling matrix diagonalization for tight-binding calculations of large copper clusters. |
Wednesday, March 7, 2018 3:18PM - 3:30PM |
P18.00005: Accurate simulation of weakly-Bound Dipole Anions Can Ataca, Hongxia Hao, Brenda Rubenstein We currently demonstrated that quantum Monte Carlo (QMC) techniques accurately predict dipole-bound anions. First theorized to exist by Fermi, dipole-bound anions are molecules that possess dipoles sufficiently strong to trap a loosely-bound electron. They can be thought of as the anionic counterparts of the Rydberg atoms. From the theoretical standpoint, modeling/predicting dipole-bound anions is particularly challenging because the energies with which they bind electrons are incredibly small: binding energies of 10-200 cm-1 make the difference between molecules that can bind electrons and those that cannot. Methods capable of describing these species must therefore deliver <10cm-1 accuracies at costs manageable for large aromatic molecules, a central challenge for any electronic structure method. With our simulations on a variety of dipole bound species, we have demonstrated that QMC methods (including variational, diffusion and auxiliary field monte carlo) can reproduce experimental binding energies with accuracy equal to or even better than more computationally demanding quantum chemistry methods such as CCSD. |
Wednesday, March 7, 2018 3:30PM - 3:42PM |
P18.00006: Quantum Optimal Control of Interacting Multi-Rotor Systems Alicia Magann, Linhan Chen, Tak-San Ho, Herschel Rabitz Efficient computational methods are needed to simulate the control of many-body quantum systems, whose total Hilbert space dimensions scale exponentially with the number of degrees of freedom present. This “curse of dimensionality” means that exact calculations are often intractable for systems of interest, and to move forward, we must introduce approximations into quantum control simulations. In this talk, I will discuss my work applying approximate computational methods to study quantum control of many interacting molecular rotors. The assumptions and tradeoffs underlying the approximations will be explained and situated in a broader context, with emphasis given to their potential relevance to other classes of quantum systems. Finally, I will review the key results of my work, which illustrate that a diverse collection of control objectives can be achieved in multi-rotor systems using a single, global control field. |
Wednesday, March 7, 2018 3:42PM - 3:54PM |
P18.00007: Bayesian Calibration assisted by Markov Chain Monte Carlo sampling of parameter space of J and U values in DFT+U: Applications for Fe, Mn and Cu based compounds Pedram Tavadze, Thomas Harris, David Mebane, Aldo Romero Density Functional Theory (DFT) fails to accurately determine the properties of strongly correlated materials (SCMs). One way to solve this problem is to add an additional Hubbard-like term (DFT+U). The strength of the on-site Coulomb and the on-site exchange interactions can be described by U and J parameters, respectively. At present, there exists no general method to evaluate these parameters for a given SCM system. These parameters are often determined using semi-empirical methods. We investigate the correlation between these parameters and the electronic density of SCMs using Bayesian Calibration assisted by Markov Chain Monte Carlo (MCMC) sampling of (U, J) parameter space for various Fe, Mn and Cu based SCMs. We also perform a comparative study of the available experimental data with the results of our theoretical calculations obtained using three different exchange correlation functionals, namely PBE, PBEsol and LDA, implemented in the VASP code. After sampling the (U, J) parameter space, we use the MCMC model to introduce an electronic density dependence of J and U values. This model can be further generalized to predict correct properties of SCMs without a need of tuning J and U values semi-empirically. |
Wednesday, March 7, 2018 3:54PM - 4:06PM |
P18.00008: Relative Energies and Electronic Structure of CoO Polymorphs Through ab-Initio Diffusion Quantum Monte Carlo Method Kayahan Saritas, Jaron Krogel, Fernando Reboredo Density Functional Theory (DFT) is currently the most popular and versatile method for atomic scale modeling and rational design of new materials. However, transition metal oxides are particularly problematic for DFT, due to the strong many-body interactions in the d-orbitals. Recently developed DFT functionals, such as SCAN, improve over the performance of LDA and PBE, but we find that they still fail to identify rocksalt as the most stable polymorph of CoO. Although DFT calculations can be adjusted by empirical parameters, such as Hubbard-U, the transferability of these parameters is questionable. Diffusion Monte Carlo (DMC) is a method that treats electrons explicitly, solving the many-body Schrödinger equation with minimum approximations. In this presentation, we will discuss our recent application of DMC methods on CoO polymorphs. We report equation of state and quasiparticle gaps data, showing that DMC is able to predict correct energetic ordering between the polymorphs. We discuss the relative importance of the errors in DMC and compare different methods in the literature used to evaluate pseudopotentials. |
Wednesday, March 7, 2018 4:06PM - 4:18PM |
P18.00009: Time Step Bias Improvement in Fixed-Node Diffusion Monte Carlo : a Size Consistent and System Independent Solution Ye Luo Simulations of realistic materials with fixed-node diffusion Monte Carlo (DMC) are becoming appealing for its comparable accuracy with high level quantum chemistry methods and much less computational cost for large systems. In this method, ground state is accessed by applying a series of short time propagators which introduce a bias. The usual way to reduce this bias is by performing calculations at a few time steps and extrapolate the measured properties to zero time step. In practice, properties like binding energy can be made less sensitive to this bias if size consistency is ensured in the method and the expensive calculations for extrapolation can be avoided. The work by A. Zen et al. [1] introduced a scheme to improve the size consistency of the branching term in the DMC algorithm and our work further improves it by making it system independent. In addition, we also study the size consistency of DMC when pseudo-potentials and T-moves [2] are used. |
Wednesday, March 7, 2018 4:18PM - 4:30PM |
P18.00010: Magnetic Moment of particles at finite temperature and density Samina Masood Electromagnetic properties of charged particles are modified at high temperatures and densities and the mass change has a significant effect on the magnetic moment of particles. We compute statistical contribution of magnetic moment of particles as a function of temperature and chemical potential. We further investigate how this change in magnetic moment shows some direct impact on the particle processes in relevant physical systems. |
Wednesday, March 7, 2018 4:30PM - 4:42PM |
P18.00011: Strong-Coupling Model for Pulsed Light Propagation and Quantum Kinetics of Driven Electron-Hole Plasma in Quantum Wires Danhong Huang, Jeremy Gulley A self-consistent quantum-kinetic model is proposed for studying the strong coupling between ultrafast carrier-scattering dynamics in photo-excited electron-hole plasma in quantum wires and the resonant scattering of an ultrashort light pulse incident on quantum wires. The individual electron and hole distributions in momentum space are further driven by an applied DC electric field along the wires, including a resistive force for momentum relaxation due to intrinsic phonon and Coulomb scattering of photo-excited carriers. Facilitated by a localized longitudinal electromagnetic field, the applied DC field is able to effectively modify an induced transverse polarization field as a quantum back-action of electrons on the propagating light pulse. This strong-coupling model allows us to study a fascinating correlation between the localized electronic response of quantum wires and the spatial-temporal features and phases of the scattered light pulses. Additionally, this strong-coupling theory also makes it possible to reveal a unique correlation between the DC current from the driven electron-hole plasma and the localized longitudinal electromagnetic field due to induced long-lasting plasma oscillations in quantum wires. |
Wednesday, March 7, 2018 4:42PM - 4:54PM |
P18.00012: Magnetic Exchange Couplings from Fermi-Löwdin Orbital Self-Interaction Corrected Density Functional Approximations Rajendra Joshi, Kushantha Withanage, Kai Trepte, Koblar Jackson, Juan Peralta Self-interaction error in density functional theory (DFT) has been well known for a long time, and its consequences on magnetic properties have been discussed in the literature. In this work, we analyze the effect of self-interaction correction in calculated magnetic exchange couplings of molecular magnets using the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method. We show that, for the systems considered, using FLO-SIC correction to DFT significantly improves calculated magnetic exchange couplings. |
Wednesday, March 7, 2018 4:54PM - 5:06PM |
P18.00013: Analytic Interatomic Forces in the Random Phase Approximation Benjamin Ramberger, Georg Kresse The random phase approximation (RPA) is a perturbational approach to evaluate the ground state energy of matter. It is growing popular recently as it describes many systems more realistically than density functional theory (DFT). However, in condensed matter simulations, forces beyond DFT have been rarely available, thus limiting the application of other methods like the RPA. Here we present our recent advances on the computation of interatomic forces in the RPA, including the work in PRL 118, 106403 (2017). There we show that the first derivative of the RPA energy with respect to the Green's function is the self-energy in the G^{0}W^{0}, which allows us to write compact equations for the RPA forces and calculate them efficiently. Furthermore, position dependent overlap operators are incorporated in the present framework, allowing us to implement the RPA forces in the projector augmented wave (PAW) formalism. We also sketch that our approach could be easily adapted for other methods like second-order Møller-Plesset (MP2) perturbation theory. Finally we give examples of recent applications, e.g. assesing the quality of different density functionals with RPA molecular dynamics [PRL 119, 145501 (2017)]. |
Wednesday, March 7, 2018 5:06PM - 5:18PM |
P18.00014: Applying Distortion Symmetries to the Calculation of Minimum Energy Pathways in Ferroelectric Switching Jason Munro, Haricharan Padmanabhan, Vincent Liu, Long-Qing Chen, Brian VanLeeuwen, H. Akamatsu, Venkatraman Gopalan, Ismaila Dabo The nudged elastic band method is a commonly used algorithm to determine the minimum energy path between the initial and final state of a kinetic process. However, these calculated pathways are critically dependent on the choice of the initial path, necessitating many trials with different starting points in order to obtain accurate minimum energy pathway predictions. Most commonly, these have been produced by applying perturbations to individual structures along the initial path. Recently, a better approach to the problem has been formulated by considering a path’s distortion symmetry group.[1] Using these, exploration of additional pathways is enabled through the generation of symmetry-adapted perturbations to the initial path. This new approach has been implemented into a Python module, and the open-source Quantum-ESPRESSO software package. It has then been used in the calculation of minimum energy pathways for bulk polarization switching and domain-wall motion in various ferroelectric materials including Ca_{3}Ti_{2}O_{7}, BiFeO_{3}, and LiNbO_{3}. The method not only successfully reproduces previously reported paths, but has also led to the discovery of hidden pathways that reveal a variety of notable physical phenomena. |
Wednesday, March 7, 2018 5:18PM - 5:30PM |
P18.00015: Gaussian process based optimization of molecules and solids using noisy energy surfaces from Quantum Monte Carlo Paul Kent, Andreas Tillack, Richard Archibald Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo. Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional numerical optimization methods that assume deterministic results. Additionally, gradients are expensive to compute to very high statistical accuracy near an energy minima, where the energy surfaces are flat. Furthermore, gradients are not yet available for some methods. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We apply these methods to non-trivial but still low dimensional problems such as simple molecules and bulk solids. Compared to traditionally applied methods, they are able to converge faster when the surfaces are not quadratic and the statistical sampling of the energy surfaces can be performed rapidly in parallel. |
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