Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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%.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: math