Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H4: Recent Advances in quantum Monte Carlo Simulations |
Hide Abstracts |
Sponsoring Units: DCOMP DCMP DMP Chair: Richard Martin, University of Illinois at Urbana-Champaign Room: Colorado Convention Center Korbel 2B-3B |
Tuesday, March 6, 2007 8:00AM - 8:36AM |
H4.00001: Recent advances in auxiliary-field methods --- simulations in lattice models and real materials Invited Speaker: We have developed an auxiliary-field (AF) quantum Monte Carlo (QMC) method for many-body simulations. The method takes the form of a linear superposition of independent-particle calculations in fluctuating external fields. ``Entanglement'' of the different field configurations leads to random walks in Slater determinant space. We formulate an approximate constraint on the random walk paths to control the sign/phase problem, which has shown to be very accurate even with simple mean-field solutions as the constraining trial wave function. The same method can be applied to both simplified lattice models and real materials. For realistic electronic Hamiltonians, each random walk stream resembles a density-functional theory (DFT) calculation in random local fields. Thus, the AF QMC method can directly import existing technology from standard electronic structure methods into a many-body QMC framework. We have demonstrated this method with calculations in close to 100 systems, including Si solid, first- and second-row molecular systems, molecules of heavier post-d elements, transition-metal systems, and ultra-cold atomic gases. In these we have operated largely in an automated mode, inputting the DFT or Hartree-Fock solutions as trial wave functions. The AF QMC results showed consistently good agreement with near-exact quantum chemistry results and/or experiment. I will also discuss additional algorithmic advances which can further improve the method in strongly correlated systems. \\ \\ Supported by ARO, NSF, ONR, and DOE-cmsn. [Preview Abstract] |
Tuesday, March 6, 2007 8:36AM - 9:12AM |
H4.00002: Lattice regularized diffusion Monte Carlo method Invited Speaker: We introduce a lattice regularization scheme for quantum Monte Carlo calculations of realistic electronic systems$[1]$. Our method is based on the discretization of a projection operator (Green's function), constructed upon an effective regularized Hamiltonian$[2]$. In particular, its Laplacian is discretized with two incommensurate mesh sizes, $a$ and $a^\prime$, where $a^\prime/a$ is a fixed irrational number, and the regularized Hamiltonian goes to the continuous limit for $a\to 0$. The use of the double mesh improves significantly the convergence to the $a\to 0$ limit, and allows one to take into account efficiently the different length scales in the system. Another advantage of this framework is the possibility to include non-local potentials in a consistent variational scheme, substantially improving both the accuracy and the computational stability upon previous non-variational diffusion Monte Carlo approaches. However, we have recently shown$[3]$ that also the standard diffusion Monte Carlo algorithm can be made stable and variational even in the presence of non-local pseudopotentials, by including a non-local discrete process in the diffusion operator. This work can open the route for even more reliable and accurate electronic ground state calculations using diffusion Monte Carlo methods. \\ \\ $[1]$ M. Casula, C. Filippi, and S. Sorella, Phys. Rev. Lett. {\bf 95}, 100201 (2005). \\ $[2]$ S. Sorella, cond-mat/0201388. \\ $[3]$ M. Casula, Phys. Rev. B {\bf 74}, 161102(R) (2006). [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:48AM |
H4.00003: Pfaffian wave functions and topology of fermion nodes Invited Speaker: Pfaffian is defined as a signed sum of all pair partitions of even number of elements and it can be viewed as a nontrivial generalization of determinant. Pfaffian enables to define the simplest possible antisymmetric wave function based on pair spinorbital(s) and therefore represents a pairing generalization of the Slater determinant of one-particle orbitals. Pfaffians actually accomodate several types of pairing wave functions, for example, one special case is the Bardeen-Cooper- Schrieffer wave function. Using this platform we propose pfaffian wave functions with simultaneous pairings both in singlet and triplet channels and we benchmark their performance in fixed-node quantum Monte Carlo. We implement Gaussian elimination-like algorithm which enables to calculate pfaffians with efficiency similar to calculation of determinants. For a testing set of first row atoms and molecules we show that single pfaffians provide correlation energies systematically at the level of about 95\%. Linear combinations of small number of pfaffians recover another fraction of the missing correlation energy comparable to significantly larger determinantal expansions. In addition, we show that pfaffians possess an important property of fermionic wave functions, namely, the minimal number of two nodal domains defined by fermion nodes. This is related to the proof that under rather general conditions closed-shell ground state wave functions of fermionic systems in d$>$1 have two nodal domains for arbitrary system size. The explicit proofs cover a number of paradigmatic models such as fermions on a sphere surface, in a periodic box, atomic states, etc, and we discuss the implications of this on efficient construction of wave functions and on several types of many-body effects. Supported by NSF and done in collaboration with M. Bajdich, L.K. Wagner, G. Drobny, and K.E Schmidt.\newline Refs: L. Mitas, PRL 96, 240402 (2006); L. Mitas, cond-mat/0605550; M. Bajdich et al, PRL 96, 130201 (2006); cond-mat/0610850. [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:24AM |
H4.00004: QMC simulations using backflow correlated wave functions Invited Speaker: An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. Backflow transformations are compact parametrizations, by which we mean that the number of parameters required to retrieve a given fraction of the correlation energy increases only slowly with system size. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for a number of systems and study the computational cost of using backflow wave functions. Backflow transformations alter the nodal surface of the wave function and can therefore be used to reduce the fixed-node error in DMC calculations. Applications to the homogeneous electron gas, the all-electron lithium atom and dimer, and carbon atom and dimer, and pseudopotential calculations for the carbon atom and dimer and carbon diamond are presented. When the initial nodal surface is reasonably accurate, backflow appears to do an excellent job in improving the VMC energy and correcting the remaining errors in the nodal surface. When the initial nodal surface is poor, however, backflow is apparently incapable of making the gross changes to the nodal surface required to correct the flaws, although it still normally lowers both the VMC and DMC energies significantly. Overall, we find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. This approach is of considerable generality as it is successful in metals and in insulators, and in large and small systems. Backflow transformations can readily be used with pairing wave functions, and this approach could yield significant improvements when a wave function consisting of a single determinant of one-particle orbitals is a poor starting point. [Preview Abstract] |
Tuesday, March 6, 2007 10:24AM - 11:00AM |
H4.00005: Resonating Valence Bond wavefunctions for electronic simulations Invited Speaker: We discuss several progress for the simulation of strongly correlated electrons, based on an efficient implementation of the Resonating Valence Bond (RVB) theory with Quantum Monte Carlo (QMC). Due to very important advances[1] in the energy optimization of strongly correlated variational wave functions, it is now possible to optimize several variational parameters with remarkable efficiency even within a stochastic approach such as QMC. In this way it is possible to describe very accurately the electronic correlation by a first principle many-body wave function, that can be extended to fairly large electronic systems. Indeed a remarkable improvement of the Hartree-Fock theory is provided by the so called RVB wave function introduced by P.W. Anderson in the context of High-Tc superconductivity[2]. For instance, by means of this paradigm, it has been possible to perform a realistic and accurate simulation of the benzene dimer, where we have found that the RVB correlation of the benzene ring plays a crucial role in the dimer bonding[3,4]. Finally we consider the still controversial low-temperature and high-pressure phase diagram of Hydrogen by using the same RVB wavefunction. We use a novel second order Langevin dynamics by introducing a consistent friction tensor, allowing to remain in thermal equilibrium even with very noisy forces, namely determined by QMC with very short runs. This allows us to simulate finite temperature systems ($\simeq 100$ H) with very high efficiency, while the variational parameters are consistently optimized during the ionic dynamics. \begin{description} \item{[1]} See C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella and R. G. Hennig, cond-mat/0611094 and references therein. \item{[2]} P. W. Anderson Science 235, 1196 (1987). \item{[3]} M. Casula, C. Attaccalite and S. Sorella J. Chem. Phys. {\bf 121} 7110 (2004). \item{[4]} S. Sorella, M. Casula and D. Rocca in preparation. \item{[5]} C. Attaccalite and S. Sorella in preparation. \end{description} [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700