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This work contains pedagogical articles on the dominant non-stochastic methods of microscopic many-body theories: density functional theory, coupled cluster theory, and correlated basis functions methods in their widest sense. Further articles introduce students to applications of these methods in front-line research such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics of current relevance. The volume aims to address the striking lack of pedagogical reference literature that allows researchers to acquire the requisite physical insight and technical skills. It should, therefore, not only serve as a collection of information relevant to those who attended the school, but provide useful reference material to a broad range of theoretical physicists in condensed matter and nuclear theory.
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Series on Advances in Quantum Many-Body Theory - Vol. 7 INTRODUCTION TO MODERN METHODS OF QUANTUM MANY-BODY THEORY AND THEIR APPLICATIONS I Editors Adelchi Fabrocini Stefano Fantoni Eckhard Krotscheck World Scientific m INTRODUCTION TO MODERN METHODS OF QUANTUM MANY-BODY THEORY AND THEIR APPLICATIONS This page is intentionally left blank Series on Advances in Quantum Many-Body Theory - Vol. 7 INTRODUCTION TO MODERN METHODS OF QUANTUM MANY-BODY THEORY AND THEIR APPLICATIONS Editors Adelchi Fabrocini University ofPisa, Italy Stefano Fantoni National Institute for Advanced Studies, Italy Eckhard Krotscheck Johannes-Kepler University, Austria \3g World Scientific wk New Jersey • LondonSingapore • Sine • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. INTRODUCTION TO MODERN METHODS OF QUANTUM MANY-BODY THEORY AND THEIR APPLICATIONS Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-238-069-8 Printed in Singapore by Mainland Press CONTENTS PREFACE xi Chapter 1 D E N S I T Y F U N C T I O N A L THEORY 1. Introduction 1.1. Units and notation 1.2. Hartree-Fock theory 1.3. Homogeneous electron gas 1.3.1. Free electrons 1.3.2. Exchange energy 2. What is density functional theory? 2.1. Hohenberg-Kohn theorem 2.2. A simple example: the Thomas-Fermi theory 2.2.1. Variational equation of Thomas-Fermi theory 2.2.2. Thomas-Fermi atom 2.2.3. An example 3. Kohn-Sham theory 3.1. Local density approximation 3.2. Spin and the local spin density approximation 3.3. The generalized gradient approximation 4. Numerical methods for the Kohn-Sham equation 4.0.1. Exact exchange 4.0.2. 0(N) methods 5. Some applications and limitations of DFT 5.1. Two examples of condensed matter 5.2. Vibrations 5.3. NMR chemical shifts 6. Limitations of DFT 7. Time-dependent density functional theory: the equations 7.1. Optical properties 7.1.1. /-sum rule 7.2. Methods to solve the TDDFT