Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session W21: General Theory: Electronic Structure and Interactions |
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Sponsoring Units: DCOMP Chair: Richard Scalettar, University of California, Davis Room: Colorado Convention Center 106 |
Thursday, March 8, 2007 2:30PM - 2:42PM |
W21.00001: Spectral-product representations of atomic and molecular Hamiltonians P.W. Langhoff, R.J. Hinde, J.D. Mills, J.A. Boatz An alternative approach to {\it ab initio} computational studies of the electronic structure of matter is described. Antisymmetry restrictions are enforced subsequent to construction of the Hamiltonian matrix for an atom or molecule in an orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer enforces the requirements of the Pauli principle, and eliminates the unphysical (non-Pauli) states spanned by the product basis. Results identical with conventional use of prior basis-state antisymmetry are obtained in applications to many-electrons atoms. For polyatomic molecules, the development accommodates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry, providing a new exact atomic-pair representation of polyatomic Hamiltonian matrices. Illustrative applications to the well-known low-lying doublet and quartet states in the H$_{3}$ molecule demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including seams of conical intersection. The calculated energy surfaces are found to be in good agreement with corresponding accurate values obtained from valence-bond and higher-level computational procedures. [Preview Abstract] |
Thursday, March 8, 2007 2:42PM - 2:54PM |
W21.00002: A Quantum Monte Carlo study of Molecular Hydrogen adsorbed on Benzene Todd D. Beaudet, Jeongnim Kim, Michele Casula, Richard M. Martin, Simone Chiesa Many prospective hydrogen storage systems contain carbon scaffolding comprised of benzene-like structural units. The binding energy of H$_2$ with these benzene-like rings is below the $\sim$ 0.2-0.4 eV/H$_2$ target necessary for reversible adsorption$^1$. Here we study the hydrogen-benzene system using quantum Monte Carlo (MC) methods suitable for resolving small energy differences. Potential energy curves are calculated using correlated umbrella sampling and variational MC. Reptation MC calculations are also in progress. A Jastrow correlated geminal wave function previously applied to benzene$^2$ is compared to Slater-Jastrows with orbitals derived from the PBE and B3LYP density functionals. We compare our results to previous work$^3$ and discuss our progress on larger systems that may have the desired binding affinity. \\ \\ $[1]$ R. C. Lochan and M. Head-Gordon, Phys. Chem. Chem. Phys. 8, 1357 (2006). \\ $[2]$ M. Casula, C. Attaccalite, and S. Sorella, J. Chem. Phys. 121, 7110 (2004). \\ $[3]$ S. Hamel and M. C\^ot\'e, J. Chem. Phys. 121, 12618 (2004). [Preview Abstract] |
Thursday, March 8, 2007 2:54PM - 3:06PM |
W21.00003: Quantum Monte Carlo study of equilibrium phase stability of crystalline FeO J. Kolorenc, L. Mitas, A. Kollias, K. Esler, R. E. Cohen We investigate phase stability of crystalline FeO at experimental equilibrium volume by means of several approaches. It is well known that energy ordering of the B1 (rocksalt) and the inverse B8 (NiAs) structures is reversed in standard DFT methods when compared to experiment. Therefore, we consider more advanced DFT-based band structure techniques, such as hybrid exchange-correlation functionals and LDA+U, and use the corresponding set of orbitals as an input for quantum Monte Carlo wave functions. We compare the results from these calculations and discuss the reasons for the DFT difficulties in describing the correct ground state of this solid. [Preview Abstract] |
Thursday, March 8, 2007 3:06PM - 3:18PM |
W21.00004: Continuum Mechanics of An Inhomogeneous System Jianmin Tao, Giovanni Vignale Starting from the hydrodynamical form of the Heisenberg equations of motion, we develop the continuum mechanics of inhomogeneous quantum many-body systems subject to weak time-dependent external potentials. The formalism allows excitation energies and transition currents to be obtained from the solution of an eigenvalue problem. First, we express the noninteracting kinetic part of the stress tensor in terms of the ground-state density and the transition current exactly, while leaving the correlation part treated approximately with the assumption of local isotropy of the correlation hole. Then we treat the linear response of the exchange part employing the first-order perturbation theory. The resulting eigenvalue problem is a fourth-order differential equation. This theory is exact for one-electron systems and expected to be accurate for many-electron systems. [Preview Abstract] |
Thursday, March 8, 2007 3:18PM - 3:30PM |
W21.00005: Ground state spin of a Fermi system with random interactions Vladimir Zelevinsky Consider a small fermionic system in a spherically symmetric field (external or self-consistent). As an example, atomic nuclei or atoms in a trap can be taken. Let the particles interact through all possible randomly selected but rotationally invariant two-body interactions. The random interaction amplitudes $V_{L}$ for the channels with all possible angular momenta $L$ of the pair are taken from an ensemble symmetric with respect to the sign of the amplitudes. As a statistical result of many realizations of the ensemble, in spite of the fact that the states with total angular momentum zero appear with a small multiplicity among all many-body states of the system, the system prefers the ground state spin zero with large probability. The probability of the maximum possible spin is also enhanced compared to pure statistical expectations. We discuss underlying physics in relation to ideas of quantum chaos and geometric chaoticity of angular momentum coupling in mesoscopic systems. [Preview Abstract] |
Thursday, March 8, 2007 3:30PM - 3:42PM |
W21.00006: Numerical Linked-Cluster Algorithms for Quantum Lattice Models Tyler Bryant, Marcos Rigol, Rajiv R. P. Singh We discuss recently introduced Numerical Linked-Cluster (NLC) Algorithms that allow one to obtain temperature dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and {\it kagom\'e} lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLC, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), High Temperature Expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte-Carlo (QMC) simulations. For many models and properties NLC results are substantially more accurate than HTE and ED. [Preview Abstract] |
Thursday, March 8, 2007 3:42PM - 3:54PM |
W21.00007: A study of a nonuniform, non-interacting electron gas in two dimensions. Michael Koivisto, M. J. Stott The study of an impurity in a two dimensional, non-interacting electron gas (Zaremba, et. al., Phys. Rev. Lett. 90, 046801 (2003)) shows significant simplifications over the three dimensional case. Linear response theory appears to have a wide range of validity even when the potential is sufficiently attractive to bind an electron. We have carried out an investigation of this two dimensional case, and studied both the electron density and energy associated with the impurity for cases of both attractive and repulsive potential. The significance of the results for density functional theory for a two dimensional system of fermions is investigated. [Preview Abstract] |
Thursday, March 8, 2007 3:54PM - 4:06PM |
W21.00008: Study of two-dimensional interacting electrons under the renormalized-ring-diagram approximation Xin-Zhong Yan, C. S. Ting The renormalized-ring-diagram approximation (RRDA) is an important approximation for investigating interacting electrons system. It is a challenge to understand the theoretical behavior of a two dimensional electron gas (TDEG) under this approximation. So far, this has never been done in the strong- coupling regime. With a super-high-efficient numerical algorithm, we self-consistently solve the integral equations for the electron Green’s function under RRDA in a TDEG with long-range Coulomb interactions from weak to strong couplings. In our numerical calculation, the equations are solved at the imaginary Matsubara frequency, so we avoid dealing with singularities in the Green's function with real frequency. Our momentum convolution is computed with the Fourier transform into real space, so reducing the two-dimensional calculation to a one-dimensional one. By so doing, the momentum-integral can be performed precisely. The obtained ground-state energy is found to be in excellent agreement with that of the Monte Carlo simulation. We will also present the numerical results of the self-energy, the effective mass, the distribution function, and the renormalization factor of the Green's function for the coupling constants in a wide range. [Preview Abstract] |
Thursday, March 8, 2007 4:06PM - 4:18PM |
W21.00009: The Holstein polaron: coupling to multiple phonon branches Mona Berciu, Lucian Covaci We extend a recently developed approach, the Momentum Average approximation, to study polaron properties when the electron couples to two or more phonon branches through Holstein-like terms. The efficient numerical procedure we propose for obtaining the Green's function within this approximation allows the accurate calculation of physical properties for a wide range of parameters and in any dimension. Our results are exact in limiting cases of very weak and very strong couplings, and accurate in the intermediate regime. This is demonstrated by studying the sum rules of the spectral function, the first 6 of which are satisfied exactly. We present results for the polaron ground state energy, quasiparticle weight, average number of phonons in the ground state and effective mass, as well as spectral functions. These are all readily calculated for a wide range of momenta and a wide range of couplings. An ansatz allowing efficient generalizations to more phonon branches will also be presented. [Preview Abstract] |
Thursday, March 8, 2007 4:18PM - 4:30PM |
W21.00010: The Green's Funciton of the Holstein Polaron Glen Goodvin, Mona Berciu, George Sawatzky I will present a novel, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. It is obtained by summing all of the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling, and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. I will then use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies. [Preview Abstract] |
Thursday, March 8, 2007 4:30PM - 4:42PM |
W21.00011: A uniform algebraically-based approach to computational physics and efficient programming James Raynolds, Lenore Mullin We present an approach to computational physics in which a common formalism is used both to express the physical problem as well as to describe the underlying details of how computation is realized on arbitrary multiprocessor/memory computer architectures. This formalism is the embodiment of a generalized algebra of multi-dimensional arrays (A Mathematics of Arrays) and an efficient computational implementation is obtained through the composition of of array indices (the psi-calculus) of algorithms defined using matrices, tensors, and arrays in general. The power of this approach arises from the fact that multiple computational steps (e.g. Fourier Transform followed by convolution, etc.) can be algebraically composed and reduced to an simplified expression (i.e. Operational Normal Form), that when directly translated into computer code, can be mathematically proven to be the most efficient implementation with the least number of temporary variables, etc. This approach will be illustrated in the context of a cache-optimized FFT that outperforms or is competitive with established library routines: ESSL, FFTW, IMSL, NAG. [Preview Abstract] |
Thursday, March 8, 2007 4:42PM - 4:54PM |
W21.00012: Transverse Quantum Noise in Landau-Zener Transition. Bogdan Dobrescu, Valery Pokrovsky, Deqiang Sun We derive master equation for quantum noise in Landau-Zener transition starting from microscopic Hamiltonian, obtain general analytical solution of the master equation and analyze most important limiting cases. [Preview Abstract] |
Thursday, March 8, 2007 4:54PM - 5:06PM |
W21.00013: Finite Size Scaling with Gaussian Basis Sets Sabre Kais, Winton Moy, Pablo Serra We have developed the finite size scaling method, which is based on taking the number of elements in a complete basis set as the size of the system,to calculate the critical parameters for a given quantum system using Gaussian basis sets. We studied the Yukawa potential and Helium-like systems by expanding the system with a Gaussian basis. The finite size scaling approach was then used with the ab initio methods to find the critical parameters of atomic and molecular systems. [Preview Abstract] |
Thursday, March 8, 2007 5:06PM - 5:18PM |
W21.00014: Data Parallel Real Symmetric Eigensolver for Approximate Eigen-Solutions in SCF Yihua Bai, Guoping Zhang Solving large real symmetric eigenvalue problems is a demanding and time consuming task in electronic structure calculations. For example, when using the Su-Schrieffer-Heeger(SSH) model to study the fundamental properties of trans-polyacetylene (trans- PA), as well as many other materials, the size of Hamiltonian matrix increases with the chain length of the material and can become very large. A data parallel divide-and-conquered eigensolver has been developed for eigen-decomposition of real symmetric matrices with strong locality properties like those generated from trans- PA, that is, matrix elements with larger magnitudes are closer to the diagonal. This eigensolver computes the approximate eigen-solutions of real symmetric matrices to user prescribed accuracy tolerance. Performance tests show that this new implementation scales up well and is extremely efficient for the computation of electronic spectrum of trans-PA compared to traditional dense eigensolvers. In some cases, the savings is order of magnitude, with the potential of saving significant amount of computation time in iterative methods like SCF. [Preview Abstract] |
Thursday, March 8, 2007 5:18PM - 5:30PM |
W21.00015: Conductance and transmission times of electrons and electromagnetic wave packets Pedro Pereyra, Herbert Simajuntak We study the conductance and transmission times of electrons and electromagnetic wave packets through semiconductor superlattices and optical superlattices, respectively. We follow the space- time evolution (described by the Schr\"odinger or Maxwell equations) of Gaussian packets with centroid at resonance, in a gap or opaque region and at the edge between the gap and the allow band. The time spent by the wave packets inside the potential region, or the optical structures, agrees extremely well with the phase time predictions and the superluminal experimantal results. [Preview Abstract] |
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