An Introduction to Quantum Monte Carlo Methods

An Introduction to Quantum Monte Carlo Methods

Tao Pang
ISBN: 9781681740454 | PDF ISBN: 9781681741093
Copyright © 2017 | 80 Pages | Publication Date: December, 2016

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Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the diffusion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analyzed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the diffusion and path-integral Monte Carlo or a recipe for developing new research in reader’s own area. Two complete Java programs, one for the diffusion Monte Carlo of 4He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption. There will also be additions to the existing programs and they are all accessible through the author's web page: http://www.physics.unlv.edu/~pang

Table of Contents

1 Introduction
1.1 Sampling
1.2 Random-number generators

2 The Metropolis algorithm
2.1 Importance sampling
2.2 Classical liquids
2.3 Block algorithms

3 Variational Monte Carlo
3.1 Variational principle
3.2 The Metropolis step
3.3 Kinetic energy and wavefunction
3.4 Quantum dots

4 Diffusion Monte Carlo
4.1 The algorithm
4.2 Evaluation of physical quantities
4.3 4He clusters on a graphite surface

5 Path-integral Monte Carlo
5.1 Introduction
5.2 The propagation of a quantum state
5.3 Single-particle system
5.4 Quantum many-body systems
5.5 Physical properties of extended systems
5.6 Cold atom

About the Author(s)

Tao Pang, University of Nevada, Las Vegas (UNLV)
Tao Pang is Professor of Physics at the University of Nevada, Las Vegas (UNLV). Following his higher education at Fudan University, one of the most prestigious institutions in China, he obtained his Ph.D. in condensed matter theory from the University of Minnesota in 1989. He then spent two years as a Miller Research Fellow at the University of California, Berkeley, before joining the UNLV physics faculty in the fall of 1991. He has been Professor of Physics at UNLV since 2002. His main areas of research include condensed matter theory and computational physics.


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