Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session W24: Electronic Structure Methods V |
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Sponsoring Units: DCOMP Chair: Eric Shirley, National Institute of Standards and Technology Room: 203AB |
Thursday, March 5, 2015 2:30PM - 2:42PM |
W24.00001: Finding Symmetry-adapted Wannier Functions from $L_1$ Sparse Optimization Jiatong Chen, Ke Yin, Yi Xia, Vidvuds Ozolins, Stanley Osher, Russel Caflisch Wannier functions have applications in numerous fields of condensed matter physics, from polarization and orbital magnetization to topological insulators and linear-scaling methods for electronic structure calculations. We present a technique to calculate symmetry-adapted Wannier functions that are strictly localized within a finite region based on the framework of compressed Wannier modes [V. Ozolins, R. Lai, R. Caflisch, S. Osher. Proc. Natl. Acad. Sci. USA 2014 111 (5) 1691-1696]. Our method does not require a prior computation of the band structure, but directly minimizes a functional that is the sum of the total energy and an $L_1$ regularization term $\frac{1}{\mu} \int | \psi| d{\bf r}$, which drives strict localization. One parameter $\mu$ controls the trade-off between the localization and the energy accuracy. Here we show how symmetry constraints can be incorporated in this formalism, leading to Wannier functions that form irreducible representations of the crystal group. Since only ${\bf k}$ points from the irreducible wedge of the Brillouin zone need to be considered, the computational effort is similar to that required for conventional band structure calculations. [Preview Abstract] |
Thursday, March 5, 2015 2:42PM - 2:54PM |
W24.00002: a new approach to Hohenberg-Kohn theorem Paul Lammert The Hohenberg-Kohn theorem is a cornerstone of electronic density functional theory, and yet in order to carry through its proof one must assume that ground state wavefunctions never vanish on a set of nonzero Lebesgue measure. This is a particularly unsatisfactory situation since DFT is supposed to avoid needing knowledge of the many-body wavefunction. I propose a new approach which puts conditions only on the density and potentials. This approach allows a proof that if the density is continuous and nowhere vanishing, then a representing potential in $L^2 + L^\infty$ is unique up to an overall constant. [Preview Abstract] |
Thursday, March 5, 2015 2:54PM - 3:06PM |
W24.00003: Enhanced transferability for Bethe-Salpeter Calculations Eric L. Shirley We have systematized projector-augmented-wave methods to reliably augment plane-wave/pseudopotential Bloch functions in atomic core regions for purposes of performing screening calculations, evaluating transition matrix elements, and evaluating Slater integrals in the condensed matter environment. This has improved the accuracy of core-hole screening, adherence to sum rules, and control of the strength of absorption features. This also ensures that transition matrix elements and concomitant core excitation spectra are reliable over significant energy ranges. To accomplish this, we improve the quality of the pseudopotentials (which become harder), extending norm conservation, and increasing the number of ``valence electrons.'' We present results for both insulators and metals, and for both core and valence excitations. Comparison to experimental data is a key part of this work. We also emphasize what approximations remain to be tackled in the treatment of electronic excitation spectra, many of which are more difficult to treat than what is within the scope of this work. [Preview Abstract] |
Thursday, March 5, 2015 3:06PM - 3:18PM |
W24.00004: A convergence test of the full potential KKR method G.M. Stocks, Yang Wang The full-potential Korringa-Kohn-Rostoker (KKR) method is a powerful tool for the ab initio study of the electronic structure of solids. In this method, the expansion of crystal wavefunctions, the LDA potential, and the charge density are determined by three angular momentum parameters respectively. Essentially, these three angular momentum parameters are an important key for controlling the convergence of an electronic structure calculation. In this presentation, we demonstrate the convergence character of the full potential KKR method by running the electronic structure calculation for a set of transition metals. We will discuss the implication of the results, and show the optimal choice of the angular momentum parameters, which are the one that requires the least computational cost for the desired accuracy for the total energy. [Preview Abstract] |
Thursday, March 5, 2015 3:18PM - 3:30PM |
W24.00005: Convergence of quasiparticle self-consistent GW calculations of transition metal monoxides Suvadip Das, John E. Coulter, Efstratios Manousakis We have investigated the electronic structure of the transition metal monoxides MnO, CoO, and NiO in their undistorted rock-salt structure within a fully iterated quasiparticle self-consistent GW (QPscGW) scheme. We have studied the convergence of the QPscGW method, i.e., how the quasiparticle energy eigenvalues and wavefunctions converge as a function of the QPscGW iterations, and compared the converged outputs obtained from different starting wavefunctions. We found that the convergence is slow and that a one-shot G$_0$W$_0$ calculation does not significantly improve the initial eigenvalues and states. In some cases the ``path'' to convergence may go through energy band reordering which cannot be captured by the simple initial unperturbed Hamiltonian. When a fully iterated solution is reached, the converged density of states, band-gaps and magnetic moments of these oxides are found to be only weakly dependent on the choice of the starting wavefunctions and in reasonable agreement with the experiment. [Preview Abstract] |
Thursday, March 5, 2015 3:30PM - 3:42PM |
W24.00006: Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory Alexandre Martin, Marc Torrent, Razvan Caracas A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives [1]. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).\\[4pt] [1] D.R Hamman et al., Phys. Rev. B 71, 035117 (2005) [Preview Abstract] |
Thursday, March 5, 2015 3:42PM - 3:54PM |
W24.00007: Constructing Wannier functions with automatically selected trial orbitals Jamal I. Mustafa, Sinisa Coh, Marvin L. Cohen, Steven G. Louie Maximally localized Wannier functions (MLWFs) are widely used in electronic structure theory. Some applications include analysis of chemical bonding, electric polarization, orbital magnetization, and Wannier interpolation. The state of the art method for constructing MLWFs of $N$ composite bands is based on the method of Marzari and Vanderbilt (MV)\footnote{Marzari, N., and D. Vanderbilt Phys. Rev. B 56, 12847 (1997).} and is implemented in the Wannier90 code. One of the practical difficulties in constructing Wannier functions using the MV method is choosing $N$ trial orbitals with roughly the same angular character and location as the target $N$ Wannier functions. We avoid this practical difficulty with a new scheme, by starting from a large set ($M$, larger than $N$) of lowest lying atomic orbitals and then selecting an optimal subspace of $N$ trial orbitals as a starting point. We investigate this approach on silicon structures of varying complexity, as well as the topological insulator Bi$_2$Se$_3$ where construction of Wannier functions for occupied electronic states is especially hard. [Preview Abstract] |
Thursday, March 5, 2015 3:54PM - 4:06PM |
W24.00008: Faster GW total energy calculations Mzuri Handlin, Marco Govoni, Giulia Galli Accurate calculations of total energies are necessary for understanding and predicting material properties. Currently density functional theory is the most widely used method for condensed systems, but in most cases it cannot accurately treat systems with dispersion interactions. Many body perturbation theory within, e.g. the GW approximation (GW), may in principle treat dispersion interactions accurately, but at a high computational cost. A major bottleneck of standard GW calculations is the required storage and inversion of large dielectric matrices, as well as the determination of their frequency dependence; the recently developed projective dielectric eigenpotential (PDEP) algorithm together with Lanczos based techniques \footnote{T. Pham, H. Nguyen, D. Rocca and G. Galli, Phys. Rev. B 87, 155148 (2013)}\footnote{M. Govoni and G. Galli, Large scale GW calculations, submitted} avoid these problems by using a spectral decomposition of the dielectric matrix. We generalized the PDEP algorithm to efficiently compute GW total energies and we will present results for the energies of molecular crystals and solids of nanoparticles. [Preview Abstract] |
Thursday, March 5, 2015 4:06PM - 4:18PM |
W24.00009: Dielectric matrix formulation of correlation energies within the Random Phase Approximation: Inclusion of (screened) exchange effects Dario Rocca, Bastien Mussard, Georg Jansen, Janos Angyan Starting from the general expression of the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the random phase approximation (RPA) correlation energy, can also be used for alternative RPA expressions including exchange effects. Within this framework we derive equations for the correlation energy within the second order screened exchange (SOSEX), an approximate time-dependent Hartree-Fock (TDHF), and second order Moller-Plesset (MP2) levels of theory. The accuracy of these approaches can be further improved by introducing the effect of the screening to obtain an approximate formulation of the Bethe-Salpeter equation for correlation energies. The proposed formalism is particularly suitable for implementation in periodic boundary condition plane-wave codes, in particular by using a compact basis set to represent dielectric matrices [1,2]. To demonstrate the accuracy of these approaches the binding curves of several diatomic molecules will be shown. \\[4pt] [1] Y. Ping, D. Rocca, and G. Galli, Chem. Soc. Rev., 42, 2437 (2013) \\[0pt] [2] D. Rocca, J. Chem. Phys. 140, 18A501 (2014) [Preview Abstract] |
Thursday, March 5, 2015 4:18PM - 4:30PM |
W24.00010: Impurity Solvers for Dynamical Mean Field Theory using Matrix Product States Martin Ganahl, Markus Aichhorn, Patrik Thunstroem, Frank Verstraete, Karsten Held, Hans Gerd Evertz We use the Time Evolving Block Decimation (TEBD) technique for for Matrix Product States to calculate spectral functions of impurity models. The resolution of the spectral function is improved using linear prediction. We apply the method as an impurity solver within the Dynamical Mean Field Theory (DMFT) for the single and two-band Hubbard model on the Bethe lattice. For the single band model we observe sharp features at the inner edges of the Hubbard bands. A finite size scaling shows that they remain present in the thermodynamic limit. We analyze the real time-dependence of the double occupation after adding a single electron and observe oscillations at the same energy as the sharp feature in the Hubbard band, indicating that they correspond to a long-lived, coherent superposition of eigenstates with different occupations. For a two-band Hubbard model we observe distinct features in the Hubbard bands which we interpret as multiplets originating from Hund's exchange. [Preview Abstract] |
Thursday, March 5, 2015 4:30PM - 4:42PM |
W24.00011: Implementation of parameter-free LDA+DMFT and GW+DMFT for diatomic molecules using exact double-counting correction Juho Lee, Kristjan Haule Dynamical Mean Field Theory (DMFT) in combination with Local Density Approximation (LDA) is widely used in solids to predict properties of correlated systems. Here one of the simplest strongly correlated systems, the hydrogen molecule H$_2$, is used as a testbed to develop a parameter-free LDA+DMFT framework. We propose a method to calculate the exact intersection of LDA and DMFT that leads to highly accurate subtraction of the doubly counted correlation in both methods. The total energy accuracy of LDA+DMFT in its single site version is around 0.3\%, provided that a good projector to the correlated subspace and the exact double-counting treatment are used. In addition to LDA+DMFT, we also implement combined GW and DMFT for diatomic molecules. The total energy accuracy of GW+DMFT is as remarkable as that of LDA+DMFT is, while the excitation spectrum is predicted in even better agreement with the exact theory. [Preview Abstract] |
Thursday, March 5, 2015 4:42PM - 4:54PM |
W24.00012: Non-adiabatic exchange-correlation kernel for the non-equilibrium response of three-dimensional Hubbard model Shree Ram Acharya, Nisha Baral, Volodymyr Turkowski, Talat S. Rahman We apply Dynamical Mean-Field Theory (DMFT) to calculate the non-adiabatic (frequency-dependent) exchange-correlation kernel for the three-dimensional Hubbard model. We analyze the dependence of the kernel on the electron doping, local Coulomb repulsion and frequency by using three different impurity solvers: Hubbard-I, Iterative Perturbation Theory (IPT) and Continuous-Time Quantum Monte Carlo (CT-QMC). From the calculated data, we obtain approximate analytical expressions for the kernel. We apply the exact numerical and analytical kernels to study the non-equilibrium response of the system for applied ultrafast laser pulse. We demonstrate that the non-adiabaticity of the kernel plays an important role in the system response; in particular, leading to new excited-states involved in the system dynamics. [Preview Abstract] |
Thursday, March 5, 2015 4:54PM - 5:06PM |
W24.00013: Machine learning for many-Body physics Louis-Francois Arsenault, Alejandro Lopez-Bezanilla, O. Anatole von Lilienfeld, Andrew J. Millis We investigate the application to many-body physics of Machine Learning (ML) methods for predicting new results from accumulated knowledge. We show that ML can be used efficiently for the Anderson impurity model (AIM)[1] and present preliminary results on its use as a solver for dynamical mean field theory (DMFT). We establish that the best representation of the Green's function for ML is by parametrizing it as an expansion in term of Legendre polynomials [1]. In DMFT applications, a key issue is the choice of descriptor, the data representation used as input for ML, which is not dependent on the impurity solver. Different parametrizations are examined. The ability to distinguish metallic and Mott insulating solutions is analysed.\\[4pt] [1] L.-F. Arsenault et al., PRB 90, 155136 (2014) [Preview Abstract] |
Thursday, March 5, 2015 5:06PM - 5:18PM |
W24.00014: Low scaling algorithms for the random phase and $GW$ approximation Merzuk Kaltak, Jiri Klimes, Georg Kresse The computationally most expensive step in conventional RPA implementations is the calculation of the independent particle polarizability $\chi_0$. We present an algorithm that calculates $\chi_0$ using the Green's function in real space and imaginary time. In combination with optimized non-uniform frequency and time grids the correlation energy on the random phase approximation level can be calculated efficiently with a computational cost that grows only cubically with system size [1,2]. We apply this approach to calculate RPA defect energies of silicon using unit cells with up to $250$ atoms and $128$ CPU cores. Furthermore, we show how to extent the algorithm to the $GW$ framework of Hedin and solve the Dyson equation for the Green's function with the same computational effort. \\[4pt] [1] M. Kaltak, J. Klime\v{s}, and G. Kresse, Journal of Chemical Theory and Computation 10, 2498-2507 (2014). \newline [2] M. Kaltak, J. Klime\v{s}, and G. Kresse, Phys. Rev. B 90, 054115 (2014). [Preview Abstract] |
Thursday, March 5, 2015 5:18PM - 5:30PM |
W24.00015: Self-consistent GW(QP)+Vertex calculations for the insulating oxides of transition (rare earth) metals Andrey Kutepov, Vladimir Antropov, Sergey Savrasov, Gabriel Kotliar Searching for a methodology with predictive power we have developed recently a new approach incorporating many-body vertex corrections into GW-based numerical schemes. Here we apply it to study the electronic structure of the following materials: SrTiO3, TiO2, NiO, and CeO2. We compare four different variations of the scheme: GW, GW+Vertex, QP (quasi-particle), and QP+Vertex. All calculations have self-consistency, at either the full or the QP level. Whereas vertex corrected GW approximation only partially corrects the GW results the QPGW approximation supplemented with first order vertex corrections to both polarizability and self energy allows us to improve essentially the agreement between calculated and experimental spectra. The addition of vertex correction diagrams to the GW method is straightforward. We discuss the subtleties involved in the addition of vertex corrections to the QPGW method. Formally our approach can be considered as fully self-consistent GW(QP)+DMFT method with a perturbative impurity solver and the implications for GW(QP)+DMFT will be discussed. [Preview Abstract] |
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