Basic Aspects Of The Quantum Theory Of Solids

This page intentionally left blank BASIC ASPECTS OF THE QUANTUM THEORY OF SOLIDS Order and Elementary Excitations Aimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems. Diverse topics such as the general theory of phase transitions, harmonic and anharmonic lattices, Bose condensation and superfluidity, modern aspects of magnetism including resonating valence bonds, electrons in metals, and strong electron correlations, are treated using the unifying concepts of order and elementary excitations. The main theoretical tools used to treat these problems are introduced and explained in a simple way, and their applications are demonstrated through concrete examples. daniel i. khomskii is a Professor in the II Physikalisches Institut, Cologne University. His main research interests are the theory of systems with strongly correlated electrons, metal–insulator transitions, magnetism, orbital ordering and superconductivity. BASIC ASPECTS OF THE QUANTUM THEORY OF SOLIDS Order and Elementary Excitations DANIEL I. KHOMSKII CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521835213 © D. Khomskii 2010 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2010 ISBN-13 978-0-511-78832-1 eBook (EBL) ISBN-13 978-0-521-83521-3 Hardback ISBN-13 978-0-521-54292-0 Paperback 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. Contents Foreword and general introduction page ix 1 Some basic notions of classical and quantum statistical physics 1 1.1 Gibbs distribution function and partition function 1 1.2 Thermodynamic functions 2 1.3 Systems with variable number of particles; grand partition function 4 2 General theory of phase transitions 6 2.1 Second-order phase transitions (Landau theory) 6 2.2 (Weak) First-order phase transitions 11 2.2.1 Another possibility of getting a first-order phase transition