Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session H23: Classical and Quantum Monte Carlo I |
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Sponsoring Units: DCOMP Chair: Pui-Man Lam, Southern University Room: C125-C126 |
Tuesday, March 16, 2010 8:00AM - 8:12AM |
H23.00001: Phase diagram and critical behavior of the square-lattice Ising model with competing nearest- and next-nearest-neighbor interactions Junqi Yin, David Landau Using the parallel tempering algorithm and GPU accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising (lattice gas) model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Possibility of the XY-like transition is examined and both transitions from the $(2\times1)$ and row-shifted $(2\times2)$ ordered phases to the paramagnetic phase turn out to be continuous. From our data analysis, reentrance behavior of the $(2\times1)$ critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the non-universal critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold. [Preview Abstract] |
Tuesday, March 16, 2010 8:12AM - 8:24AM |
H23.00002: Nodal structures and analytical properties of many-body wavefunctions for quantum Monte Carlo Lubos Mitas The node of many-body stationary wavefunction is the set of configurations for which the wavefunction vanishes. Its accuracy plays an important role in quantum Monte Carlo methods where it enables to avoid the fermion sign problem in the fixed-node approximation simulations. We investigate several aspects of fermion nodes. In particular, we elucidate the analytical properties of nodes and their relationship to quantities such as kinetic and total energies. We study how nodal locus errors impact the local energy distributions and their asymptotic properties. We also study the nodes of fermionic excited states and their topologies in comparison with the ground states. [Preview Abstract] |
Tuesday, March 16, 2010 8:24AM - 8:36AM |
H23.00003: Finite Size Scaling of Melting in Two Dimensions Keola Wierschem, Efstratios Manousakis We study the melting transition of a two-dimensional Lennard-Jones fluid using classical Monte Carlo simulation techniques. We perform a finite-size scaling analysis within the context of the KTHNY theory of melting, which expects melting to occur via a two-stage process, with separate transitions for translational and orientational order. Careful attention is paid to the fact that there are two order parameters, and the behavior of their correlation lengths across the transition region. [Preview Abstract] |
Tuesday, March 16, 2010 8:36AM - 8:48AM |
H23.00004: Quantum Monte Carlo backflow calculations of the benzene dimer Kathleen Schwarz, Richard Hennig Benzene dimers provide the prototypical system for weak pi-pi interactions that determine the bonding for various organic materials and carbon nanostructures. Several previous studies using coupled-cluster, symmetry adapted perturbation theory, and quantum Monte Carlo methods have determined the binding energies of various configurations of the benzene dimer. In this work we investigate the accuracy of different trial wave functions for variational and diffusion Monte Carlo calculations for a set of candidate ground state dimer geometries. We compare Slater, Slater Jastrow, Slater Jastrow Backflow, and Multi-determinant wave functions. The inclusion of backflow improves our VMC and DMC total energies more than orbital optimization, larger basis sets, and increasing the number of determinants in the trial wave function. Using Slater Jastrow Backflow wave functions, we calculate the binding energies of the benzene dimers. [Preview Abstract] |
Tuesday, March 16, 2010 8:48AM - 9:00AM |
H23.00005: A generalization of valence-bond-Monte-Carlo to spin 1 magnets Andreas Deschner, Erik S. Sorensen Valence-bond-Monte-Carlo is an elegant and efficient projective Monte-Carlo method that has been employed to calculate ground-state properties of bipartite antiferromagnets. Until now it has only been used for spin 1/2 models. We propose a method that allows one to also treat spin 1 models with valence-bond-Monte-Carlo. The spin 1 Heisenberg antiferromagnet with nearest-neighbour-interaction is used as an example to explain the method and to show its usefulness for bipartite spin 1 models. [Preview Abstract] |
Tuesday, March 16, 2010 9:00AM - 9:12AM |
H23.00006: Geometry optimization using Quantum Monte Carlo Lucas Wagner, Jeffrey Grossman One of the long-lasting challenges in Quantum Monte Carlo (QMC) has been to find minimum energy structures efficiently, particularly for the projector Monte Carlo methods. The primary obstacles to this goal are the difficulty of calculating efficient and accurate gradients of the energy and the inherent stochastic nature of the algorithm, which is shared with many other interesting solution methods. We are particularly interested in the case of electronic structures of realistic systems, where for many interesting systems such as excited states, weak-binding, and transition metal oxides, the traditional methods based on DFT are not acceptably accurate. We present an algorithm that is well behaved in the presence of known noise and finds the minimum energy structure quickly. The Hessian matrix at the minimum is calculated simultaneously, and gradient information, if available, is easily and consistently included. [Preview Abstract] |
Tuesday, March 16, 2010 9:12AM - 9:24AM |
H23.00007: Large scale application of kinetic ART, a near order-1 topologically- based off-lattice kinetic Monte-Carlo algorithm with on-the-fly calculation of events Laurent Karim Beland, Fedwa El-Mellouhi, Normand Mousseau Using a topological classification of events\footnote{B. D. McKay, Congressus Numerantium 30, 45 (1981).} combined with the Activation-Relaxation Technique (ART nouveau) for the generation of diffusion pathways, the kinetic ART (k-ART)\footnote{F. El-Mellouhi, N. Mousseau and L. J. Lewis, Phys Rev B, 78,15 (2008).} lifts many restrictions generally associated with standard kinetic Monte Carlo algorithms. In particular, it can treat on and off-lattice atomic positions and handles exactly long-range elastic deformation. Here we introduce a set of modifications to k-ART that reduce the computational cost of the algorithm to near order 1 and show applications of the algorithm to the diffusion of vacancy and interstitial complexes in large models of crystalline Si (100 000 atoms). [Preview Abstract] |
Tuesday, March 16, 2010 9:24AM - 9:36AM |
H23.00008: Introducing the Reduced Monte Carlo Scheme (RMCS): Application to ideal quantum gases and classical hard sphere systems Uduzei Edgal The development of a new Monte Carlo scheme is provided -- the Reduced Monte Carlo Scheme (RMCS). The term ``reduced'' is used because only a small number of particles (n) is needed in the simulation for accurate calculation of material properties. Ie., n $>\sim $ 10. The fundamental ensemble used as basis for the scheme is the canonical ensemble. The power and efficiency of RMCS is demonstrated by reproducing well known results for the statistical thermodynamic properties of ideal quantum systems (Fermi and Bose cases) and the classical hard sphere system at all densities. [Preview Abstract] |
Tuesday, March 16, 2010 9:36AM - 9:48AM |
H23.00009: Systematic reduction of sign errors in many-body calculations of atoms and molecules P.R.C. Kent, M. Bajdich, M.L. Tiago, R.Q. Hood, F.A. Reboredo We apply the self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf 79} 195117 (2009), ibid. {\bf 80} 125110 (2009)] to the calculation of ground states of atoms and molecules. By comparing with configuration interaction results we show the method yields systematic convergence towards the exact ground state wave function and reduction of the fixed-node DMC sign error. We present results for atoms and light molecules, obtaining, e.g. the binding of N$_2$ to chemical accuracy. Moreover, we demonstrate that the algorithm is robust enough to be used for the systems as large as the fullerene C$_{20}$ starting from a set of random coefficients. SHDMC thus constitutes a practical method for systematically reducing the Fermion sign problem in electronic structure calculations. Research sponsored by the ORNL LDRD program (MB), U.S. DOE BES Divisions of Materials Sciences \& Engineering (FAR, MLT) and Scientific User Facilities (PRCK). LLNL research was performed under U.S. DOE contract DE-AC52-07NA27344 (RQH). [Preview Abstract] |
Tuesday, March 16, 2010 9:48AM - 10:00AM |
H23.00010: Systematic reduction of sign errors for excited states in many-body problems Fernando Reboredo A recently developed self-healing diffusion Monte Carlo algorithm (SHDMC) is extended to the calculation of excited states. SHDMC is a recursive approach that improves systematically the nodes of the trial wave function by locally smoothing the kinks of the fixed-node wave function [Reboredo, Hood and Kent PRB {\bf 79}, 195117 (2009)]. The smoothed-fixed-node wave-functions of inequivalent nodal pockets of excited states are estimated simultaneously from the mixed probability density. The decay of the wave-function into lower energy states is avoided by i) removing the projection of the improved trial-wave function into previously calculated eigenstates; and ii) adjusting the reference energy in each nodal pocket. It is demonstrated, in a model system, that the algorithm converges to many-body excited states in bosonic and fermionic cases [Reboredo PRB {\bf 80}, 125110 (2009)]. The computational cost of SHDMC scales linearly with the number of independent degrees of freedom of the nodal surface, while its accuracy improves systematically with the nodal degrees of freedom and as the statistical data collected increases. [Preview Abstract] |
Tuesday, March 16, 2010 10:00AM - 10:12AM |
H23.00011: Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations Frank Petruzielo, Julien Toulouse, Cyrus Umrigar Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states. For calculations requiring non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that behave as Gaussians at short distances and Slaters at long distances. These basis functions further improve the energy and fluctuations of the local energy for a given basis size. Gains achieved by exponent optimization and Gauss-Slater basis use are exemplified by variational Monte Carlo calculations for the ground state of carbon, the lowest lying excited states of carbon with $^5S^o$, $^3P^o$, $^1D^o$, $^3F^o$ symmetries, and carbon dimer. Basis size reduction enables quantum Monte Carlo treatment of larger molecules at high accuracy. [Preview Abstract] |
Tuesday, March 16, 2010 10:12AM - 10:24AM |
H23.00012: Transient quantum Monte Carlo investigations of few-electron systems Norm Tubman, Jonathan Dubois, Randolph Hood, Berni Alder Diffusion Monte Carlo (DMC) is one of the most accurate methods for calculating electronic structure and can be applied to systems containing thousands of electrons. Typical applications of DMC utilize the fixed-node approximation, in which the nodes are specified using an input trial wave function. Errors in the locations of the nodes lead to systematic errors in DMC energy estimators. Removing this nodal bias can be done using transient quantum Monte Carlo methods, which have previously been applied to the free-electron gas and a handful of other few-electron systems. The drawback in using transient methods is the significant increase in computational cost. We have studied several quantum systems of varying sizes in order to better understand the scaling properties of various transient methods. We have explored techniques for reducing the computational cost such as cancellation and correlated walkers. We have analyzed our data using Bayesian inference. Prepared by LLNL under Contract DE-AC52-07NA27344 [Preview Abstract] |
Tuesday, March 16, 2010 10:24AM - 10:36AM |
H23.00013: A quantum Monte Carlo study of a spherical jellium with an embedded impurity Michal Bajdich, Fernando A. Reboredo, G. Malcolm Stocks, Paul R.C. Kent, Jeongnim Kim We study the effects of a model impurity in a spherical jellium with quantum Monte Carlo (QMC) methods. The closed-shell energies and densities of jellium spheres have been studied previously using density functional theory (DFT) as well as QMC methods~[1,2]. In this study, we begin by reproducing the previous results. Second, we add an impurity to model the transition between de-localized jellium states and localized atomic-like states in correlated metallic systems. We obtain the phase space diagram of the system using Hartree--Fock, several DFT approximations and QMC methods. The differences between methods are further analyzed by comparing the ground state densities. Finally, using the inverse susceptibility scheme, we obtain the effective exchange-correlation potential and compare it with exciting approximations of DFT. \\[4pt] [1] L. M. Almeida et. al., Phys. Rev. B {\bf 66}, 075115 (2002).\\[0pt] [2] F. Sottile et. al., Phys. Rev. B {\bf 64}, 045105 (2001) and P. Ballone et. al,. Phys. Rev. B {\bf 45}, 6293 (1992). [Preview Abstract] |
Tuesday, March 16, 2010 10:36AM - 10:48AM |
H23.00014: Construction of localized wave functions for a disordered optical lattice and analysis of the resulting Hubbard model parameters Shengquan Zhou, David Ceperley We propose a method to construct localized single particle wave functions using imaginary time projection and thereby determine lattice Hamiltonian parameters. We apply the method to a specific disordered potential generated by an optical lattice experiment and calculate for each instance of disorder, the equivalent lattice model parameters. The probability distributions of the Hubbard parameters are then determined. Tests of ocalization and energy convergence are examined. [Preview Abstract] |
Tuesday, March 16, 2010 10:48AM - 11:00AM |
H23.00015: Study of the dynamic behavior of Niedermayer's algorithm Daniel Girardi, Nilton Branco We calculate the dynamic exponent for the
Niedermayer algorithm applied to the two-dimensional Ising and
$XY$ models,
for various values of the free parameter $E_0$.
For $E_0=-1$ we reobtain the Metropolis algorithm and for $E_0=1$
we regain the Wolff algorithm. For $-1 |
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