## Quantum Monte Carlo Methods in Physics and ChemistryM.P. Nightingale, Cyrus J. Umrigar In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published. |

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### Contents

Basics quantum Monte Carlo and statistical mechanics | 1 |

Stochastic dagonalization | 37 |

Worldline quantum Monte Carlo | 65 |

Variational Monte Carlo in solids | 101 |

Variational Monte Carlo basics and applications to atoms and molecules | 129 |

Calculations of exchange frequenceis with path integral Monte Carlo solid 3 He adsorbed on graphite | 161 |

Static response of homogeneous quantum fluids by diffusion Monte Carlo | 183 |

Equilibrium and dynamical path integral methods an introduction | 213 |

Quantum Monte Carlo in nuclear physics | 287 |

Reptation quantum Monte Carlo | 313 |

Quantum Monte Carlo for lattice fermions | 343 |

Phase separation in the 2D Hubbard model a challenging application of fixednode QMC | 375 |

Constrained path Monte Carlo for fermions | 399 |

Serial and parallel random number generation | 425 |

Fixednode DMC for fermions on a lattice application to doped fullerides | 447 |

463 | |

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Quantum Monte Carlo Methods in Physics and Chemistry M.P. Nightingale,Cyrus J. Umrigar Limited preview - 1998 |

### Common terms and phrases

algorithm applications approximation atoms average bosons boundary conditions calculations Chem classical compute configurations convergence coordinates correlation function corresponding CPMC D.M. Ceperley defined density matrix diagonal diffusion Monte Carlo dimension discussed distribution dynamics eigenstate eigenvalue equation estimate evaluate exact expectation value exponential fermion finite fixed-node fluctuations Fourier given Green's function ground ground-state energy Hamiltonian hopping Hubbard model importance sampling interaction Jastrow factor Kalos lattice Lett linear M.P. Nightingale many-body matrix elements Monte Carlo methods nodes obtained ODLRO operator optimal orbitals parameter parameterization particle path integral Phys Physics potential probability propagator properties pseudopotentials pseudorandom pseudorandom number quantum Monte Carlo quasirandom random number random walk sign problem simulation single-particle Slater determinant solid spin statistical error stochastic symmetric temperature tion transition trial function trial wavefunction two-body Umrigar variance variational Monte Carlo walkers wave function wavefunction weight world-line zero

### Popular passages

Page iii - Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA A three-dimensional dynamic trap for confining a collisional neutral gas is described.