### 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 language | English (US) |
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Title of host publication | Lecture Notes in Physics |

Publisher | Springer Verlag |

Pages | 401-476 |

Number of pages | 76 |

Volume | 936 |

DOIs | |

State | Published - 2017 |

### Publication series

Name | Lecture Notes in Physics |
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Volume | 936 |

ISSN (Print) | 0075-8450 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*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