Variational and diffusion monte carlo approaches to the nuclear few- and many-body problem

Francesco Pederiva, Alessandro Roggero, Kevin Schmidt

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

We review Quantum Monte Carlo methods, a class of stochastic methods allowing for solving the many-body Schrödinger equation for an arbitrary Hamiltonian. The basic elements of the stochastic integration theory are first presented, followed by the implementation to the variational solution of the quantum many-body problem. Projection algorithms are then introduced, beginning with a formulation in coordinate space for central potentials, in order to illustrate the fundamental ideas. The extension to Hamiltonians with an explicit dependence on the spin-isospin degrees of freedom is then presented by making use of auxiliary fields (Auxiliary Field Diffusion Monte Carlo, AFDMC). Finally, we present the Configuration Interaction Monte Carlo algorithm (CIMC) a method to compute the ground state of general, local or non-local, Hamiltonians based on the configuration space sampling.

Original languageEnglish (US)
Title of host publicationLecture Notes in Physics
PublisherSpringer Verlag
Pages401-476
Number of pages76
Volume936
DOIs
StatePublished - 2017

Publication series

NameLecture Notes in Physics
Volume936
ISSN (Print)0075-8450

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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    Pederiva, F., Roggero, A., & Schmidt, K. (2017). Variational and diffusion monte carlo approaches to the nuclear few- and many-body problem. In Lecture Notes in Physics (Vol. 936, pp. 401-476). (Lecture Notes in Physics; Vol. 936). Springer Verlag. https://doi.org/10.1007/978-3-319-53336-0_9