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.

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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Utility depends on need
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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Magnetic Ions in Crystals
K.W.H. Stevens
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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Book Description

There have been many demonstrations, particularly for magnetic impurity ions in crystals, that spin-Hamiltonians are able to account for a wide range of experimental results in terms of much smaller numbers of parameters. Yet they were originally derived from crystal field theory, which contains a logical flaw; electrons on the magnetic ions are distinguished from those on the ligands. Thus there is a challenge: to replace crystal field theory with one of equal or greater predictive power that is based on a surer footing. The theory developed in this book begins with a generic Hamiltonian, one that is common to most molecular and solid state problems and that does not violate the symmetry requirements imposed on electrons and nuclei. Using a version of degenerate perturbation theory due to Bloch and the introduction of Wannier functions, projection operators, and unitary transformations, Stevens shows that it is possible to replace crystal field theory as a basis for the spin-Hamiltonians of single magnetic ions and pairs and lattices of magnetic ions, even when the nuclei have vibrational motion. The power of the method is further demonstrated by showing that it can be extended to include lattice vibration and conduction by electron hopping such as probably occurs in high-Tc superconductors. Thus Stevens shows how an apparently successful ad hoc method of the past can be replaced by a much more soundly based one that not only incorporates all the previous successes but appears to open the way to extensions far outside the scope of the previously available methods. So far only some of these have been explored. The book should therefore be of great interest to all physicists and chemists concerned with understanding the special properties of molecules and solids that are imposed by the presence of magnetic ions.

Quantum Many-Body Systems in One Dimension (Series on Advances in Statistical Mechanics, Vol 12)

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Quantum Many-Body Systems in One Dimension (Series on Advances in Statistical Mechanics, Vol 12)
Zachary Nyong-Chol Ha
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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Book Description

The main theme of the book is focused on the intimate connection between two families of exactly solvable models: the inverse-square (ISE) and the nearest-neighbor exchange (NNE) models. The NNE models are Bethe-Ansatz solvable and include the Heisenberg spin chain, t-J models and Hubbard models. The ISE Calogero-Sutherland family of models are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin-charge separation, in the context of the explicit models.

Quantum Many Particle Systems (Advanced Book Classics)

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Clear, precise, and modern
An important book for beginner cond-mat physicists and more.

Quantum Many Particle Systems (Advanced Book Classics)
John W. Negele , and Henri Orland
Manufacturer: Westview Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0738200522

Book Description

This volume explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonpurturbative approximations based on functional integrals; general arguments based on order parameters; symmetry, and Fermi liquid theory; and stochastic methods. Each approach provides its own insights and quantitative capabilities, and in conjunction provide a powerful framework for understanding a wide variety of physical systems. Written at a level for graduate students with no prior background in manybody theory, this classic text is intended for physicists in solid state physics, field theory, atomic physics, condensed matter physics, quantum chemistry, and nuclear physics.

Customer Reviews:

Clear, precise, and modern.......2002-09-11

A great physics book for field theory applied to condensed
matter and sometimes nuclear physics problems. The authors
are EXTREMELY careful mathematically and really don't skip
any steps or shove stuff under the rug; in fact, the first
chapter is just all math about how to do integrals and path
integrals and field integrals and deal with Grassman numbers.
A bit unusual for a physics book, but that's their style.

The rest of the book deals with the usual and other material:

zero-temperature Green's functions and perturbation theory
(for energy, Green's function, etc.) The treatment is detailed
and relatively exhaustive. Then there is the same for finite-
temperature. The earlier sections on linear response are
concise and one of the best treatments of the subject I have
seen leading directly to the fluctuation dissipation expression
(after this book I realized this vaunted "fluctuation-dissipation" that no one can explain is just
a straightforward thing about commutators and pert. theory).

The book also has other good stuff: a chapter on mean field theory, Landau-Ginzburg theory, order parameters, and a nice
discussion about spontaneous symmetry breaking that helps
clarify a bunch of stuff. Then there is a whole chapter on
further aspects of one-particle Green's functions (Dyson
equation, solving for poles, quasiparticles, satellites, etc.)
that is pretty good and gets the physical point across. There
is also a chapter on statistical (monte carlo, numerical, etc.)
methods for doing quantum many body problems. While some of
the methods are not the most up to date or modern, the basics
are all there (Monte Carlo, Hubbard-Strataonvich (spelling?),
inverting matrices via Monte Carlo, some stuff about lattice
systems, Langevin equation simulation for Monte Carlo, updating
problems, etc.) There is also a chapter on more advanced
functional integration stuff. Also there is a nice description
of the loop expansion and whatnot.

The book is very well written, has no errors as far as I can
tell, and is exhaustive on what it treats. The problems at
the end of the first few chapters deal with physics problems
and help build intuition whereas the texts in these chapters
are more formal. The book could use some more physical insights
sprinkled throughout, but that is not too much of a drawback.

The book is based on functional integration (Feynman integral)
methods for field theory: this is the modern way folks do it
and it is a powerful way of doing field theory both to
derive results, connect results, do expansions and what not,
and also for certain kinds of monte carl computations. So
having read this, the reader is up to date on a pretty modern
view of field theory in condensed matter (and somewhat on
nuclear physics).

Highly recommended unless you can't stand precise and long
mathematical treatments. My only misgiving is that sometimes
I wish the authors provided more physical insights for certain
concepts and gave some examples rather than "just the math";
but they do this in other parts of the book, so perhaps
my complaint, which is not that serious, is more about the
uneven way this is done. Nevertheless, this is 5/5 and a book
you will read many times and learn from many times.

An important book for beginner cond-mat physicists and more........2000-04-10

A very good introduction to the many particle systems, includes all from the basics of coherent states to very complex parts of theory.

Field Theories for Low-Dimensional Condensed Matter Systems

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Field Theories for Low-Dimensional Condensed Matter Systems

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540671773

Book Description

The contributions in this book give a high-level coverage of many of the subjects and techniques needed to understand the physics of low-dimensional condensed matter systems. The topics presented include the use of conformal field theories, the Luttinger liquid approach to one-dimensional electron systems, and the use of random matrices in problems connected with quantum chaos. The contributions are authored by some of the most prominent physicists active in the field, among them the 1998 Nobel Prize laureate R. B. Laughlin. The book should become an extremely useful instrument for all those interested in theoretical condensed matter physics.

Field Theories of Condensed Matter Systems (Advanced Books Classics)

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Field Theories of Condensed Matter Systems (Advanced Books Classics)
Fradkin
Manufacturer: Westview Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0201328593

Current Topics in Condensed Matter and Particle Physics: Non-Perturbative Phenomena and Strongly Correlated Systems : 19 May-14 June 1991 (Kathmandu Summer School Lecture Notes)

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Current Topics in Condensed Matter and Particle Physics: Non-Perturbative Phenomena and Strongly Correlated Systems : 19 May-14 June 1991 (Kathmandu Summer School Lecture Notes)
J. Pati , and Q. Shafi
Manufacturer: World Scientific Pub Co Inc
ProductGroup: Book
Binding: Hardcover

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Field Theories in Condensed Matter Physics

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Field Theories in Condensed Matter Physics

Manufacturer: Taylor & Francis
ProductGroup: Book
Binding: Paperback

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Book Description

The application of field theoretic techniques to problems in condensed matter physics has generated an array of concepts and mathematical techniques to attack a range of problems such as the theory of quantum phase transitions, the quantum Hall effect, and quantum wires. While concepts such as the renormalization group, topology, and bosonization have become necessary tools for the condensed matter physicist, enough open problems and interesting applications remain to drive much activity in this area in the coming years. Field Theories in Condensed Matter Physics presents a comprehensive survey of the concepts, techniques, and applications of the field. Written by experts and carefully edited, the book provides the necessary background for graduate students entering the area of modern condensed matter physics. It also supplies field theorists with a valuable introduction to the areas in condensed matter physics where field theoretic concepts can be fruitfully applied.

New Theoretical Approaches to Strongly Correlated Systems (Nato Science Series II: Mathematics, Physics and Chemistry, Volume 23) (NATO Science Series II: Mathematics, Physics and Chemistry)

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New Theoretical Approaches to Strongly Correlated Systems (Nato Science Series II: Mathematics, Physics and Chemistry, Volume 23) (NATO Science Series II: Mathematics, Physics and Chemistry)
Alexei M., Ed. Tsvelik
Manufacturer: Kluwer Academic Publishers
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792370007

Book Description

For many years, the physics of strongly correlated systems was considered a theorists' playground, right at the border with pure mathematics, where physicists from the `real world' did not venture. The time has come, however, when healthy physics cannot exist without these techniques and results.
Lectures on selected topics in the theory of strongly correlated systems are here presented by the leading experts in the field. Topics covered include a use of the form factor approach in low-dimensional systems, applications of quantum field theory to disorder, and dynamical mean field theory. The main divisions of the book deal with: I) Quantum Critical Points; (II) Strongly Correlated One-Dimensional Systems; (III) Strong Correlations and Disorder; and (IV) Dynamical Mean Field Theory.

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