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A pedagogical introduction to Quantum Monte-Carlo

  • Michel Caffarel
  • Roland Assaraf
Part of the Lecture Notes in Chemistry book series (LNC, volume 74)

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.

Keywords

Stochastic Matrix Monte Carlo Step Trial Vector Quantum Monte Carlo Trial Wave Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Michel Caffarel
    • 1
  • Roland Assaraf
    • 2
  1. 1.CNRS-Laboratoire de Chimie Théorique, Tour 22-23Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Scuola Internazionale Superiore di Studi Avanzati (SISSA)and Istituto Nazionale Fisica della Materia (INFM)TriesteItaly

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