(特价书)多体系统中的量子标度理论(英文版)

书籍
物理书籍
　　This is a book on quantum phase transitions (QFT), a new and exciting subject. Here we concentrate on these transitions which occur in strongly correlated electronic systems. The scaling theory of quantum critical phenomena, which is presented already in the first chapter, provides a unifying view of the quite different physical phenomena treated here as, metalinsulator instabilities and heavy fermion behavior. ...
　　

preface .
chapter 1 scaling theory of quantum critical phenomena
1.1 quantum phase transitions
1.2 renormalization group and scaling relations
1.3 the critical exponents
1.4 scaling properties close to a zero temperature fixed point
1.5 extension to finite temperatures
chapter 2 landau and gaussian theories
2.1 introduction
2.2 landau theory of phase transitions
2.3 gaussian approximation (t ] tc)
2.4 gaussian approximation (t [ tc)
2.5 goldstone mode
chapter 3 renormalization group: the e-expansion
3.1 the landau-wilson functional
3.2 the renormalization group
chapter 4 quantum phase transitions
4.1 effective action for a nearly ferromagnetic metal
4.2 the quantum paramagnetic-to-ferromagnetic transition
4.3 extension to finite temperatures

　　This is a book on quantum phase transitions (QFT), a new and exciting subject. Here we concentrate on these transitions which occur in strongly correlated electronic systems. The scaling theory of quantum critical phenomena, which is presented already in the first chapter, provides a unifying view of the quite different physical phenomena treated here as, metalinsulator instabilities and heavy fermion behavior. .
　　In the initial chapters of the book, general ideas and basic models of statistical mechanics are introduced. Although historically, the scaling approach was developped earlier, the appropriate framework to describe critical phenomena is the renormalization group (RG). The concepts of fixed points, unstable and attractors, flow in parameter space, the notion of crossover, provide the foundations for the phenomenological scaling theory. Consequently the renormalization group is carefully presented both in its momentum version and real space formulation. The way this is done is by applying these methods to specific and basic problems. For the momentum space formulation we consider the original Wilson-Landau functional and the e-expansion in the one-loop approximation. The classical (thermal) case is studied first and then the renormalization group equations for the quantum case of a ferromagnetic transition in a metal are obtained. Our presentation of the momentum space RG is given without any mention to Feynman diagrams and anywhere the reader has to appeal to appendices for going through the presentation. We think this is an advantage that allows the reader to concentrate on the essential ideas of the RG and e-expansion.
　　The real space renormalization group is presented in the block version through a study of the Ising model in a transverse field, which is our paradigm for a quantum transition. After having acquired skills in these techniques and have become familiar with the language of critical phenomena we start to investigate actual physical systems. We begin with the case of heavy fermions where the formalism and ideas developed in the previous chapters play a fundamental role to understand the physics of these systems. The concept of coherence temperature, related to a quantum critical point, is introduced and it's importance emphasized, as it represents the characteristic temperature of a Kondo lattice, in distinction to the Kondo temperature of the one-impurity problem. Once the coherence temperaturo is identified, as that below which the correlated system enters the Fermiliquid regime, the idea that electronic systems at a quantum critical point (QCP) present non-Fermi liquid behavior comes out naturally in the presentation. The thermodynamic properties of this non-Fermi liquid state are obtained, in terms of the critical exponents associated with the QCP, using scaling arguments.
　　Next we study meted-insulator transitions which occur at zero temperature. As a reference and to substantiate the scaling ideas, the classical work of Gutzwiller (Gutzwiller, 1965) on the metal-insulator (MI) transition in the Hubbard model is carefully presented and discussed. Metal-insulator transitions which occur by the effect of correlations are distinguished from density-driven MI transitions occurring by variation in the chemical potential or electron density. Here the power of the scaling approach is revealed as it allows for a deep analysis of these phenomena.
　　The non-linear sigma model is discussed next, calling attention for the importance of transverse fluctuations in systems with short range order close to the lower critical dimension. The relevance of this model for several problems in condensed matter physics justifies its study in this book. We also take here the opportunity to review and consolidate many concepts and ideas of the RG introduced previously. ..
　　The book ends with a discussion on first order zero temperature transitions. This is still a very new subject and to put it into a framework, we discuss the interesting phenomenon of fluctuation induced phase transitions in its quantum version. This is the Coleman-Weinberg mechanism (Coleman and Weinberg, 1973) which was proposed in the context of quantum field theories.
　　The subject of quantum phase transitions is a new and growing area of research. For the problems we are interested here, it is probably fair to say, it started with the seminal work of Hertz (Hertz, 1976). Since then many people have contributed to this field which reaches so many basic areas in condensed matter physics and physics in general. We do not intend to give here a complete set of references in this vast field. Fortunately an up to date bibliography on QFT has been given in the recent book by Sachdev (Sachdev, 1999).
　　This book is also, inevitably, a book on statistical mechanics. As such, it has been influenced by the books of Toulouse and Pfeuty (1975), Ma (1976), Fradkin (1991), Goldenfeld (1992), Auerbach (1994) and other classics in this field.
　　We do not address in this book the problem of high temperature superconductivity. This should not be interpreted, as if, the concepts and methods presented are not relevant to this field. In fact it may just be the contrary. However, the influence of the proximity to a quantum critical point in physical properties is much more well established for heavy fermions than for oxide superconductors. Caution kept us out from the temptation of discussing the high-Tc materials here.
　　Finally we did not investigate the effects of disorder near quantum phase transitions (Miranda, Dobrosavljevic and Kotliar, 1996; Castro Neto, Castilla and Jones, 1998). This is clearly present in the real heavy fermion systems that we are trying to understand. It may even be the basic feature determining the behavior of a class of materials involving mainly Uranium as a constituent. The experimental work and ideas here are even more recent and are evolving fast. As concerns the effect of disorder in metalinsulator transitions, this touches the immense subject of Anderson transitions, on which there are several reviews available (Lee and Ramakrishnan, 1985; Belitz and Kirkpatrick, 1994; Georges et al., 1996; Imada, Fujimori and Tokura, 1998).
　　I would like to thank the colleagues with whom I have discussed subjects of this book. Among them, G. Aeppli, S. Bud'ko, B. Coqblin, M. D. Coutinho-Filho, B. Elschner, A. Ferraz, Z. Fisk, J. Flouquet, M. Fontes, A. Lacerda, C. Lacroix, M. Lavagna, H.v. Lohneysen, A. J. Millis, L. Nunes, S. Sachdev, E. Baggio-Saitovitch, F. Steglich and J. Thompson. My sincere thanks to Amos Troper, Eduardo Miranda and Enzo Granato for enlightening discussions and several suggestions to improve the manuscript. I thank F. Nogueira for pointing out the derivation of the renormalization group equations, as presented in Chapter 3, without the use of diagrams. I also thank L. Belvedere, R. L. P. G. Amaral and N. F. Svaiter for their help on Chapter 12. Several students have collaborated in different ways to the final version of this book. In particular I thank Marcio Argollo for his interest. The author however is the sole responsible for any mistakes or omissions in the book.
　　I would like also to express my recognition for the encouragement of my parents and the friendship of Priscila and Flavio Derdyk.
　　My sincere thanks to LEPES in Grenoble, in particular to Jean-Louis Tholence, for the hospitality during the months this book was concluded. Last but not least I would like to thank the Brazilian agencies, CNPq and FAPERJ for partial financial support. ...