Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces

A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual ``bare'' estimator associated with the observable by an improved or ``renormalized'' estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a Zero-Variance Zero-Bias (ZVZB) property similar to the usual Zero-Variance Zero-Bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular systems. Calculations of the entire force curve of the H$_2$,LiH, and Li$_2$ molecules are presented. Spectroscopic constants $R_e$ (equilibrium distance) and $\omega_e$ (harmonic frequency) are also computed. The equilibrium distances are obtained with a relative error smaller than 1%, while the harmonic frequencies are computed with an error of about 10%

On the stability of Be3: A benchmark complete active space self-consistent field + averaged quadratic coupled cluster study

International audienceThe optimized geometries and binding energies for the linear and triangular isomers of the beryllium trimer have been obtained through benchmark multireference averaged quadratic coupled cluster (AQCC) calculations using very large complete active space SCF (CASSCF) references (12 active electrons in 13 and 14 orbitals). Geometries were optimized with the cc-pV5Z basis, while the binding energies (including counterpoise correction) were obtained with the significantly larger aug-cc-pV5Z basis set. The binding energies (27.3 and 16.3 kcal/mol for the equilateral and linear isomers, respectively) are larger than the previous full CI benchmark values, while the corresponding Be-Be equilibrium distances of 4.101 and 4.088 a.u. are smaller. In view of the near-size consistency character of the CASSCF + AQCC method, the fact that all 12 electrons are fully correlated, the active reference space includes 14 orbitals, and the very large basis set used here, we propose to consider these results as reference data for Be3. Using the electron pair localization function obtained at the CASSCF(12,15) level, it is clearly illustrated that the 2p orbitals lying in the molecular plane play a dominant role in the bonding pattern for the equilateral isomer

Coexistence of solutions in dynamical mean-field theory of the Mott transition

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from Quantum Monte Carlo (QMC) simulations and from the Exact Diagonalization method. I pay special attention to discretization errors within QMC. These errors explain why it is difficult to obtain the solutions by QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe

Quantum Monte Carlo calculations of electronic excitation energies: the case of the singlet n→π∗n \to \pi^* (CO) transition in acrolein

We report state-of-the-art quantum Monte Carlo calculations of the singlet $n \to \pi^*$ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouab\c{c}a {\it et al.} [J. Chem. Phys. {\bf 130}, 114107 (2009)]. We investigate the effect of using a Slater basis set instead of a Gaussian basis set, and of using state-average versus state-specific complete-active-space (CAS) wave functions, with or without reoptimization of the coefficients of the configuration state functions (CSFs) and of the orbitals in variational Monte Carlo (VMC). It is found that, with the Slater basis set used here, both state-average and state-specific CAS(6,5) wave functions give an accurate excitation energy in diffusion Monte Carlo (DMC), with or without reoptimization of the CSF and orbital coefficients in the presence of the Jastrow factor. In contrast, the CAS(2,2) wave functions require reoptimization of the CSF and orbital coefficients to give a good DMC excitation energy. Our best estimates of the vertical excitation energy are between 3.86 and 3.89 eV.Comment: 6 pages, 1 figure, 2 tables, to appear in Progress in Theoretical Chemistry and Physic

Optimization of ground and excited state wavefunctions and van der Waals clusters

A quantum Monte Carlo method is introduced to optimize excited state trial wavefunctions. The method is applied in a correlation function Monte Carlo calculation to compute ground and excited state energies of bosonic van der Waals clusters of upto seven particles. The calculations are performed using trial wavefunctions with general three-body correlations

Dynamical Mean Field Theory of the Antiferromagnetic Metal to Antiferromagnetic Insulator Transition

We study the antiferromagnetic metal to antiferromagnetic insulator using dynamical mean field theory and exact diagonalization methods. We find two qualitatively different behaviors depending on the degree of magnetic correlations. For strong correlations combined with magnetic frustration, the transition can be described in terms of a renormalized slater theory, with a continuous gap closure driven by the magnetism but strongly renormalized by correlations. For weak magnetic correlations, the transition is weakly first order.Comment: 4 pages, uses epsfig,4 figures,notational errors rectifie

Stat3 is required to maintain the full differentiation potential of mammary stem cells and the proliferative potential of mammary luminal progenitors.

Stat3 has a defined role in mammary gland where it is a critical mediator of cell death during post-lactational regression. On the other hand, Stat3 is required for the self-renewal of embryonic stem cells and is sufficient for the induction of a naïve pluripotent state in epiblast stem cells. Mammary stem cells (MaSCs) have a high capacity for self-renewal and can grow robustly in transplantation experiments in vivo. However, a role for Stat3 in MaSCs has not been investigated. Here we show that depletion of Stat3 from basal cells results in reduced primary transplantation efficiency and diminishes the potential to generate ductal, but not alveolar, outgrowths. In addition, Stat3 is required for maximal proliferation of luminal progenitors

Green's Function Monte Carlo for Lattice Fermions: Application to the t-J Model

We develop a general numerical method to study the zero temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's Function Monte Carlo, projects the ground state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional t-J model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed-shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the t-J model. We find that the most accurate results are consistent with phase separation at all interaction strengths.Comment: 22 pages, 22 figure