Quantum Monte Carlo study of Jastrow perturbation theory. I. Wave function optimization

Abstract

We have studied an iterative perturbative approach to optimize Jastrow factors in quantum Monte Carlo calculations. For an initial guess of the Jastrow factor we construct a corresponding model Hamiltonian and solve a first-order perturbation equation in order to obtain an improved Jastrow factor. This process is repeated until convergence. Two different types of model Hamiltonians have been studied for both energy and variance minimization. Our approach can be considered as an alternative to Newton’s method. Test calculations revealed the same fast convergence as for Newton’s method sufficiently close to the minimum. However, for a poor initial guess of the Jastrow factor, the perturbative approach is considerably more robust especially for variance minimization. Usually only two iterations are sufficient in order to achieve convergence within the statistical error. This is demonstrated for energy and variance minimization for the first row atoms and some small molecules. Furthermore, our perturbation analysis provides new insight into some recently proposed modifications of Newton’s method for energy minimization. A peculiar feature of the analysis is the continuous use of cumulants which guarantees size-consistency and provides least statistical fluctuations in the Monte Carlo implementation.