QUANTUM MONTE CARLO METHODS - Cambridge

Cambridge University Press 978-1-107-00642-3 - Quantum Monte Carlo Methods: Algorithms for Lattice Models J . E. Gubernatis, N. Kawashima and P. Werner Frontmatter More information

QUANTUM MONTE CARLO METHODS

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating Fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo.

j. e . g u b e r nat i s works at the Los Alamos National Laboratory. He is a Fellow of the American Physical Society (APS) and served as a Chair of the APS' Division of Computational Physics. He represented the United States on the Commission of Computational Physics of International Union of Pure and Applied Physics (IUPAP) for nine years and chaired the Commission for three years. n. k awa s h i m a is a professor at the University of Tokyo. He is a member of the Society of Cognitive Science and has been a Steering Committee member for the public use of the supercomputer at the Institute for Solid State Physics (ISSP) for the last 15 years. He received the Ryogo Kubo Memorial Prize for his contributions to the development of loop and cluster algorithms in 2002. p. w e r n e r is a professor at the University of Fribourg. In 2010, he received the IUPAP Young Scientist Prize in computational physics for the development and implementation of quantum Monte Carlo methods for impurity models.

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Cambridge University Press 978-1-107-00642-3 - Quantum Monte Carlo Methods: Algorithms for Lattice Models J . E. Gubernatis, N. Kawashima and P. Werner Frontmatter More information

? in this web service Cambridge University Press



Cambridge University Press 978-1-107-00642-3 - Quantum Monte Carlo Methods: Algorithms for Lattice Models J . E. Gubernatis, N. Kawashima and P. Werner Frontmatter More information

QUANTUM MONTE CARLO METHODS

Algorithms for Lattice Models

J . E. GUBERNATIS

Los Alamos National Laboratory

N . K AWA S H I M A

University of Tokyo

P. W E R N E R

University of Fribourg

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Cambridge University Press 978-1-107-00642-3 - Quantum Monte Carlo Methods: Algorithms for Lattice Models J . E. Gubernatis, N. Kawashima and P. Werner Frontmatter More information

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Cambridge University Press is part of the University of Cambridge. It furthers the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

Information on this title: 9781107006423

? Cambridge University Press 2016 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written

permission of Cambridge University Press. First published 2016

Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalogue record for this publication is available from the British Library

Library of Congress Cataloging in Publication data Gubernatis, J. E., author.

Quantum Monte Carlo methods : algorithms for lattice models / J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg). pages cm Includes bibliographical references and index. ISBN 978-1-107-00642-3 (Hardback : alk. paper) 1. Monte Carlo method. 2. Many-body problem. I. Kawashima, N. (Naoki), author. II. Werner, P., 1975- author. III. Title. QC174.85.M64G83 2016 530.1201 518282?dc23 2015026699 ISBN 978-1-107-00642-3 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

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Cambridge University Press 978-1-107-00642-3 - Quantum Monte Carlo Methods: Algorithms for Lattice Models J . E. Gubernatis, N. Kawashima and P. Werner Frontmatter More information

Contents

Preface

Part I Monte Carlo basics

1 Introduction 1.1 The Monte Carlo method 1.2 Quantum Monte Carlo 1.3 Classical Monte Carlo

2 Monte Carlo basics 2.1 Some probability concepts 2.2 Random sampling 2.3 Direct sampling methods 2.3.1 Discrete distributions 2.3.2 Continuous distributions 2.4 Markov chain Monte Carlo 2.4.1 Markov chains 2.4.2 Stochastic matrices 2.5 Detailed balance algorithms 2.5.1 Metropolis algorithm 2.5.2 Generalized Metropolis algorithms 2.5.3 Heat-bath algorithm 2.6 Rosenbluth's theorem 2.7 Entropy content Exercises

3 Data analysis 3.1 Equilibrating the sampling 3.2 Calculating averages and estimating errors 3.3 Correlated measurements and autocorrelation times

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