Self-consistent Quantum-Field Theory and Bosonization for Strongly Correlated Electron Systems (Lecture Notes in Physics Monographs)

Book Description

This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory. Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson systems.
Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field theoretic formulation of "bosonization" is presented; it is published here for the first time. This method is applied to the fractional quantum Hall effect, to the Coulomb plasma, and to several exactly solvable models.

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Quantum Theory of the Electron Liquid
Gabriele Giuliani , and Giovanni Vignale
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521821126

Book Description

Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book introduces the quantum theory of the electron liquid and the mathematical techniques that describe it. The electron liquid's behavior is governed by the laws of quantum mechanics which prevail over the microscopic world of atoms and molecules.

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Wonderful!.......2007-07-01

This is a kind of book rare to find nowadays. It seems to be the result of a long and careful investigation of the literature, of reflection, of deep physical understanding. It avoids hand-waving, "phenomenological", jargon and fashionable types of arguments, in favor of well grounded, logical and mathematically solid arguments. It is the opposite of most we find today, that is, it is not a set of "lectures" quickly transformed into textbook; it is not the point of view of the authors, defended by phraseology; it is not a biased book. It is really a wonderful book, very well written, displaying love by the subject, strong curiosity and search for the truth.
Congratulations to the authors! May their book inspire other physicists to search truth instead of glory and fame. May their book inspire the young to avoid the fashion and easy way. May their book become a classic because it truly deserves.

An outstanding job.......2005-10-08

Written with the student in mind, this book gives an excellent introduction to density functional theory, many-body quantum theory, and their application to the physical system now known as the electron liquid. Given the current interest in electron liquids, both from an applied and a theoretical standpoint, this book serves a need for those who want to educate themselves on the different techniques and strategies used to study the behavior of electron liquids, and general many-body systems. The authors of the book emphasize modern developments, and give many references for those readers who want to pursue the subject in even more detail. An understanding of both the physical and mathematical ideas in the book require concentrated effort, but anyone who has decided to read such a sizable book realizes that true insight into any subject only comes from such an effort. The authors understand this, and they do not hesitate to elaborate on sophisticated concepts when they arise. But they also interject informal and colloquial language in many places in the text. This serves to set the reader more at ease, and makes for even more enjoyable reading.

Readers (such as this reviewer) who have a background in high energy physics or relativistic quantum field theory will find many of the concepts used in these fields find application in the theory of electron liquids. In addition, many of the concepts used in high-energy physics, such as the idea of spontaneously broken symmetries, arose in condensed matter and many-body physics. The symbiosis of ideas between these different fields has been a fruitful one and this will no doubt continue in the years to come. An example of this is the Chern-Simons theory, which arose in the context of quantum chromodynamics as a theory of the strong interaction, and finds its way in this book in the discussion on the Laughlin theory of the fractional quantum Hall liquid. This theory, as the authors point out, is based on a careful choice of wave functions, and therefore cannot be viewed as systematic in its strategy in finding solutions. The Chern-Simons theory is brought in to provide a more systematic approach. It is a fascinating strategy, for using it one maps the problem of the two-dimensional electron liquid into an equivalent many-body problem of interacting composite particles. One can then use a mean-field approximation on the latter system. This approach is somewhat similar to the "duality" phenomena found in string theories (although the analogy is somewhat loose). The Chern-Simon theory also finds its place in purely mathematical contexts, such as topological quantum field theory and the theory of knots, and readers with a background in this area will see familiar constructions in the author's discussions. The authors derive an expression for the electromagnetic response function for a system of composite particles that satisfies Kohn's theorem, but point out that it does not have the correct scaling properties.

The authors give a thorough overview of density functional theory, with emphasis placed not only on the formalism but also on its utility in solving many-body problems. Readers growing up in the usual formalism of Hilbert spaces will need justification as to the power of density functional methods and how one can still calculate quantities of interest without really using the many-body wave function. And, anyone who has tried to perform numerical computations of quantum-mechanical quantities understands the need for algorithms that are manageable, i.e. that allow the computation of physical quantities in a reasonable time scale. The authors point out though that the Kohn-Sham equations, which result after the minimization of the energy as a functional of the electron density, can be solved computationally on a time scale that increases as a power of the number of electrons. This is to be contrasted with the computation of the solution of the N-electron Schrodinger equation, which depends exponentially on N. However, as in all problems in constrained optimization, there is no free lunch (this has been proven rigorously), and so there is always a penalty to be paid in any solution strategy. For the Kohn-Sham equations, one uses the `effective potential' that is local in space, but has a nonlocal dependence on the density, allowing only an approximate description. Another penalty arises from using the determinantal wave function in the solution of the Kohn-Sham equations does not give a robust approximation to the true ground-state wave function. The last penalty arises because of the "universal" nature of density functional: it has the same form for all physical systems and so does not bring out the physical properties that are unique to a particular one. In addition to these issues, readers who insist on constructive approaches to mathematical proof will reject the proof of the Hohenberg-Kohn theorem, since it relies on proof by contradiction. In physical applications this is a minor issue of course, but in attempts to put density functional theory, indeed all of quantum field theory, on a constructive rigorous mathematical foundation, this issue is of importance. The authors (correctly) have no intention of respecting mathematical rigor, and state so explicitly. Instead they emphasize the physics behind the formalism and discuss the experimental evidence for it. Indeed, the book is full of examples of this evidence, and the appropriate references are given. Most of the discussion on the experimental situation is given in the context of the quantum Hall effect, which seems appropriate given that the authors have made original contributions to the understanding of this effect.

[DISCLOSURE: This reviewer knows the second author personally, but did not discuss this review with him. The opinions above are an honest assessment of the content of the book, and were not influenced, at least consciously, by any personal knowledge of the author.]

Great book!!.......2005-08-06

This book is truly a valuable and unique resource for physicists and quantum chemists interested in the structure and dynamics of electronic systems, especially (but not solely) in the solid-state. It presents the standard theories, as well as very recent cutting-edge developments, for example, extensions of density functional theory to time-dependent phenomena and current-densities -- all with elegant derivations and beautiful explanations. The authors have an extremely engaging writing style, which makes the book one of the most enjoyable physics books I have read. Many of the exercises at the end of each chapter are fascinating in themselves, instructive, and clearly explained.
I feel this book will prove to be a wonderful treasure for graduate students, postdocs, and professors.

Excellent.......2005-05-02

This is the one of best overall book on the electronic theory of solids. It certainly covers all relevant aspect one could ever want to know about the topic and does a phenomenal job of clearly explaining and demonstrating the material. The best example is the chapter dedicated to the Fermi liquid with the very illuminating explanations of the theory of quasiparticles. This book is easy to read and its lecture does not require advanced mathematical knowledge. It is an excellent textbook and a very good start point for research problems. It is also remarkable the use of state of the art results and the elimination of several common misconceptions. I must say that the exercises are a good opportunity to better understand the material.

Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Graduate Texts)

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mixed

Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Graduate Texts)
Xiao-Gang Wen
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

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ASIN: 019922725X

Book Description

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.

Customer Reviews:

Utility depends on need.......2006-06-28

This book reflects the research interests of the author, who is a genius, and should not be considered introductory, even at the graduate level. I do not find this book useful for learning anything for the first time. However, it provides an interesting perspective on many classic topics in many-body theory. Unlike the previous reviewer, I found the grandious statements a wonderful feature since most textbooks lack any of the author's voice. Reading this book is closer to attending a lecture than any text of it's kind I've read. I get this book from the library and I wouldn't pay $100 for it especially since the author posts his lectures notes on his website and much of the later material can be obtained from PROLA.

mixed.......2004-08-19

This book is really awkward. There is some standard many body theory but no beginning student will be able to learn it from this book alone. Second of all there are some very awkward statements like "fermions ..behave like non-local excitations because fermions cannot be created alone." (p146)While his line of reasoning for a particular model is decently clear, the statement about the nonexistance of a lone fermion is ridiculous. He makes occaisional grandiose statements like " [his pet theory] provides and answer to the origin of light and fermions" (p9). I find the calculations sketchy at best --you can learn deep things but at great expense. overall i find this book to mix ridiculousness and obtuse reading with insight. I think it's a poor book because pedagogy should be paramount in a textbook.

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Electron Correlation in the Solid State

Manufacturer: World Scientific Publishing Company
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Binding: Hardcover

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Electron Liquid Theory of Normal Metals (Horizons in World Physics)

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Electron Liquid Theory of Normal Metals (Horizons in World Physics)

Manufacturer: Nova Science Pub Inc
ProductGroup: Book
Binding: Hardcover

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ASIN: 0941743195

Fluctuations and Localization in Mesoscopic Electron Systems

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Fluctuations and Localization in Mesoscopic Electron Systems
Martin Janssen
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810242093

Lectures on the Physics of Highly Correlated Electron Systems VII: Seventh Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors (AIP Conference Proceedings)

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Lectures on the Physics of Highly Correlated Electron Systems VII: Seventh Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors (AIP Conference Proceedings)

Manufacturer: American Institute of Physics
ProductGroup: Book
Binding: Hardcover

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ASIN: 0735401470

Book Description

The objective of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the pedagogical lectures are up-to-date monographs of relevant subjects in the field of condensed matter physics. Contributions include: polarons (the polaron concept, optical properties and internal structure of polarons, many-polaron systems, magnetoabsorption of polarons, optical properties of quantum dots: role of the polaron interaction, interacting polarons in a quantum dot, small polarons); multielectron bubbles in liquid helium: a spherical two-dimensional electron system (oscillation modes, bubble stability and fissioning, the spherical two-dimensional electron gas, the Wigner solid of electrons in the bubble); the numerical approach to the correlated electron problem: quantum Monte Carlo methods (the world line approach for the XXZ model and relation to the 6-vertex model, auxiliary field Quantum Monte Carlo algorithms, application of the auxiliary field QMC to specific Hamiltonians, the Hirsch-Fye impurity algorithm); basic models in the quantum theory of magnetism (the Heisenberg model, the Hubbard model, and the sd-model).

Nanostructures and Quantum Effects: Proceedings of the Jrdc International Symposium Tsukuba, Japan, November 17-18, 1993 (Springer Series in Materials Science)

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Nanostructures and Quantum Effects: Proceedings of the Jrdc International Symposium Tsukuba, Japan, November 17-18, 1993 (Springer Series in Materials Science)
H. Sakaki , and H. Noge
Manufacturer: Springer
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Binding: Hardcover

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Quantum Electron Liquids and High-Tc Superconductivity (Lecture Notes in Physics New Series M)

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Quantum Electron Liquids and High-Tc Superconductivity (Lecture Notes in Physics New Series M)
Miguel A. Martin-Delgado , German Sierra , and Angeles H. Vozmediano
Manufacturer: Springer
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Binding: Hardcover

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Book Description

The goal of these courses is to give the non-specialist an introduction to some old and new ideas in the field of strongly correlated systems, in particular the problems posed by the high-Tc superconducting materials. The starting viewpoint to address the problem of strongly correlated fermion systems and related issues of modern condensed matter physics is the renormalization group approach applied to quantum field theory and statistical physics. The authors review the essentials of the Landau Fermi liquid theory, they discuss the 1d electron systems and the Luttinger liquid concept using different techniques. Finally they present the basic phenomenology of the high-Tc compounds and different theoretical models to explain their behaviour.

The Quantum World Unveiled by Electron Waves

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A masterpiece of scientific writing describing beautiful experiments

The Quantum World Unveiled by Electron Waves
Akira Tonomura
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9810225105

Customer Reviews:

A masterpiece of scientific writing describing beautiful experiments.......2005-12-09

This is a wonderful book clearly describing beautiful experiments. This masterpiece of scientific writing describes fundamental phenomena in quantum mechanics, while avoiding technical jargon.

In the process of developing holography electron microscope technology, Dr. Tonomura's group has successfully visualized a number of striking quantum phenomena. The "double-slit experiment with electrons" is a classic experiment described now even in first year physics textbooks. The definite proof of the Aharonov-Bohm effect is also clearly described in this enjoyable book. Moreover, the visualization of the spatio-temporal dynamics of vortices in superconductors is also presented with clarity and sufficient details. These are all experiments pioneered in the author's laboratory.

The over-arching theme of the author, and this book, is the ability to actually see the quantum phenomena occurring at the nanoscale. This abaility is allowing an unprecedented level of understanding of quantum phenomena. Readers will be delighted with this book. It is a gem. The illustrations are illuminating and beautiful (enjoyed even by my very young daughter). This is a strongly recommended book for anyone interested in quantum mechanics.

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