Abstract
Quantum Monte Carlo (QMC) methods are powerful stochastic approaches to calculate ground-state properties of quantum systems. They have been applied with success to a great variety of problems described by a Schrodinger-like Hamiltonian (quantum liquids and solids, spin systems, nuclear matter, ab initio quantum chemistry, etc ... ). In this paper we give a pedagogical presentation of the main ideas of QMC. We develop and exemplify the various concepts on the simplest system treatable by QMC, namely a 2 x 2 matrix. First, we discuss the Pure Diffusion Monte Carlo (PDMC) method which we consider to be the most natural implementation of QMC concepts. Then, we discuss the Diffusion Monte Carlo (DMC) algorithms based on a branching (birth-death) process. Next, we present the Stochastic Reconfiguration Monte Carlo (SRMC) method which combines the advantages of both PDMC and DMC approaches. A very recently introduced optimal version of SRMC is also discussed. Finally, two methods for accelerating QMC calculations are sketched: (a) the use of integrated Poisson processes to speed up the dynamics (b) the introduction of “renormalized” or “improved” estimators to decrease the statistical fluctuations.
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© 2000 Springer-Verlag Berlin Heidelberg
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Caffarel, M., Assaraf, R. (2000). A pedagogical introduction to Quantum Monte-Carlo. In: Mathematical Models and Methods for Ab Initio Quantum Chemistry. Lecture Notes in Chemistry, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57237-1_3
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DOI: https://doi.org/10.1007/978-3-642-57237-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67631-7
Online ISBN: 978-3-642-57237-1
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