@misc{bajdich_mitas_2009, title={ELECTRONIC STRUCTURE QUANTUM MONTE CARLO}, volume={59}, ISSN={["1336-040X"]}, DOI={10.2478/v10155-010-0095-7}, abstractNote={Electronic structure quantum Monte Carlo Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.}, number={2}, journal={ACTA PHYSICA SLOVACA}, author={Bajdich, Michal and Mitas, Lubos}, year={2009}, pages={81–168} }
@article{wagner_bajdich_mitas_2009, title={QWalk: A quantum Monte Carlo program for electronic structure}, volume={228}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2009.01.017}, abstractNote={We describe QWalk, a new computational package capable of performing quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of quantum Monte Carlo methods. It is open-source, licensed under the GPL, and available at the web site http://www.qwalk.org.}, number={9}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Wagner, Lucas K. and Bajdich, Michal and Mitas, Lubos}, year={2009}, month={May}, pages={3390–3404} }
@article{bajdich_mitas_wagner_schmidt_2008, title={Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods}, volume={77}, ISSN={["1098-0121"]}, DOI={10.1103/physrevb.77.115112}, abstractNote={We investigate pfaffian trial wavefunctions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study [Bajdich et al., Phys. Rev. Lett. 96, 130201 (2006)], we explore the possibilities of expanding the wavefunction in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wavefunction based on fully antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wavefunctions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian, and essentially exact large-scale configuration interaction wavefunctions. Finally, we combine the recently proposed form of backflow correlations [Drummond et al., J. Phys. Chem. 124, 22401 (2006); Rios et al., Phys. Rev. E. 74, 066701 (2006)] with both determinantal and pfaffian based wavefunctions.}, number={11}, journal={PHYSICAL REVIEW B}, author={Bajdich, M. and Mitas, L. and Wagner, L. K. and Schmidt, K. E.}, year={2008}, month={Mar} }
@article{bajdich_mitas_drobny_wagner_schmidt_2006, title={Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations}, volume={96}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.96.130201}, abstractNote={We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.}, number={13}, journal={PHYSICAL REVIEW LETTERS}, author={Bajdich, M and Mitas, L and Drobny, G and Wagner, LK and Schmidt, KE}, year={2006}, month={Apr} }
@article{bajdich_mitas_drobny_wagner_2005, title={Approximate and exact nodes of fermionic wavefunctions: Coordinate transformations and topologies}, volume={72}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.72.075131}, abstractNote={A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two-electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^{4}S({p}^{3})$ state using appropriate coordinate maps and wave function symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into three-dimensional space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wave functions.}, number={7}, journal={PHYSICAL REVIEW B}, author={Bajdich, M and Mitas, L and Drobny, G and Wagner, LK}, year={2005}, month={Aug} }