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%

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

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

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

Interaction induced delocalisation for two particles in a periodic potential

We consider two interacting particles evolving in a one-dimensional periodic structure embedded in a magnetic field. We show that the strong localization induced by the magnetic field for particular values of the flux per unit cell is destroyed as soon as the particles interact. We study the spectral and the dynamical aspects of this transition.Comment: 4 pages, 5 EPS figures, minor misprints correcte

Hydrogel-forming microneedle arrays: Potential for use in minimally-invasive lithium monitoring

AbstractWe describe, for the first time, hydrogel-forming microneedle (s) (MN) arrays for minimally-invasive extraction and quantification of lithium in vitro and in vivo. MN arrays, prepared from aqueous blends of hydrolysed poly(methyl-vinylether-co-maleic anhydride) and crosslinked by poly(ethyleneglycol), imbibed interstitial fluid (ISF) upon skin insertion. Such MN were always removed intact. In vitro, mean detected lithium concentrations showed no significant difference following 30min MN application to excised neonatal porcine skin for lithium citrate concentrations of 0.9 and 2mmol/l. However, after 1h application, the mean lithium concentrations extracted were significantly different, being appropriately concentration-dependent. In vivo, rats were orally dosed with lithium citrate equivalent to 15mg/kg and 30mg/kg lithium carbonate, respectively. MN arrays were applied 1h after dosing and removed 1h later. The two groups, having received different doses, showed no significant difference between lithium concentrations in serum or MN. However, the higher dosed rats demonstrated a lithium concentration extracted from MN arrays equivalent to a mean increase of 22.5% compared to rats which received the lower dose. Hydrogel-forming MN clearly have potential as a minimally-invasive tool for lithium monitoring in outpatient settings. We will now focus on correlation between serum and MN lithium concentrations

Local-Ansatz Approach with Momentum Dependent Variational Parameters to Correlated Electron Systems

A new wavefunction which improves the Gutzwiller-type local ansatz method has been proposed to describe the correlated electron system. The ground-state energy, double occupation number, momentum distribution function, and quasiparticle weight have been calculated for the half-filled band Hubbard model in infinite dimensions. It is shown that the new wavefunction improves the local-ansatz approach (LA) proposed by Stollhoff and Fulde. Especially, calculated momentum distribution functions show a reasonable momentum dependence. The result qualitatively differs from those obtained by the LA and the Gutzwiller wavefunction. Furthermore, the present approach combined with the projection operator method CPA is shown to describe quantitatively the excitation spectra in the insulator regime as well as the critical Coulomb interactions for a gap formation in infinite dimensions.Comment: To be published in Phys. Soc. Jpn. 77 No.11 (2008

Guided random walk calculation of energies and <\sq {r^2} > values of the 1Σg^1\Sigma_g state of H_2 in a magnetic field

Energies and spatial observables for the $^1\Sigma_g$ state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random walk Feynman-Kac algorithm. We demonstrate that the accuracy of the results and the simplicity of the method may prove it a viable alternative to large basis set expansions for small molecules in applied fields.Comment: 10 pages, no figure

Cooperative Effect of Coulomb Interaction and Electron-Phonon Coupling on the Heavy Fermion State in the Two-Orbital Periodic Anderson Model

We investigate the two-orbital periodic Anderson model, where the local orbital fluctuations of f-electrons couple with a two-fold degenerate Jahn-Teller phonon, by using the dynamical mean-field theory. It is found that the heavy fermion state caused by the Coulomb interaction between f-electrons U is largely enhanced due to the electron-phonon coupling g, in contrast to the case with the single-orbital periodic Anderson model where the effects of U and g compete to each other. In the heavy fermion state for large $U$ and g, both the orbital and lattice fluctuations are enhanced, while the charge (valence) and spin fluctuations are suppressed. In the strong coupling regime, a sharp soft phonon mode with a large spectral weight is observed for small U, while a broad soft phonon mode with a small spectral weight is observed for large U. The cooperative effect of U and g for half-filling with two f-electrons per atom $n_f=2$ is more pronounced than that for quarter-filling with $n_f=1$.Comment: 8 pages, 11 figures, accepted for publication in JPS