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Luttinger Model
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Book Synopsis Quantum Theory of the Electron Liquid by : Gabriele Giuliani
Download or read book Quantum Theory of the Electron Liquid written by Gabriele Giuliani and published by Cambridge University Press. This book was released on 2008-06-19 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.
Book Synopsis Luttinger Model by : Vieri Mastropietro
Download or read book Luttinger Model written by Vieri Mastropietro and published by World Scientific. This book was released on 2014 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Luttinger Model is the only model of many-fermion physics with legitimate claims to be both exactly and completely solvable. In several respects it plays the same role in many-body theory as does the 2D Ising model in statistical physics. Interest in the Luttinger model has increased steadily ever since its introduction half a century ago. The present volume starts with reprints of the seminal papers in which it was originally introduced and solved, and continues with several contributions setting out the landscape of the principal advances of the last fifty years and of prominent new directions.
Book Synopsis Luttinger Model by : Vieri Mastropietro
Download or read book Luttinger Model written by Vieri Mastropietro and published by World Scientific. This book was released on 2013-10-08 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Luttinger Model is the only model of many-fermion physics with legitimate claims to be both exactly and completely solvable. In several respects it plays the same role in many-body theory as does the 2D Ising model in statistical physics. Interest in the Luttinger model has increased steadily ever since its introduction half a century ago. The present volume starts with reprints of the seminal papers in which it was originally introduced and solved, and continues with several contributions setting out the landscape of the principal advances of the last fifty years and of prominent new directions. Contents:The Luttinger Model and Its Solution:An Exactly Soluble Model of a Many-Fermion System (Joaquin M Luttinger)Exact Solution of a Many-Fermion System and Its Associated Boson Field (Daniel C Mattis and Elliott H Lieb)Lattice, Dynamical and Nonlinear Effects:Luttinger Model and Luttinger Liquids (Vieri Mastropietro)The Luttinger Liquid and Integrable Models (Jesko Sirker)Long Time Correlations of Nonlinear Luttinger Liquids (Rodrigo G Pereira)An Expanded Luttinger Model (Daniel C Mattis)Applications and Experimental Test:Quantum Hall Edge Physics and Its One-Dimensional Luttinger Liquid Description (Orion Ciftja)A Luttinger Liquid Core Inside Helium-4 Filled Nanopores (Adrian Del Maestro)Some Experimental Tests of Tomonaga–Luttinger Liquids (Thierry Giamarchi)Bosonization and Its Application to Transport in Quantum Wires (Feifei Li)Generalizations to Higher Dimensions:Fermions in Two Dimensions, Bosonization, and Exactly Solvable Models (Jonas de Woul and Edwin Langmann)Luttinger Liquid, Singular Interaction and Quantum Criticality in Cuprate Materials (Carlo Di Castro and Sergio Caprara)Luttinger Model in Dimensions d > 1 (Daniel C Mattis) Readership: Physicists and theoretical chemists in condensed matter and/or nuclear-matter physics and graduate students in these fields, mathematical physicists working in the many-body problem, experimentalists in low-dimensional phenomena. Keywords:Luttinger Model;Luttinger Liquid;Physics in One Dimention;Many-Fermion Theory;Many-Body PhysicsReviews: “Luttinger's model has come to play such a dominant role in condensed matter physics that a book like this is most welcome and long overdue. The model, which grew out of Thirring's model, is not only soluble – it is also reveals a great deal about physics that is not easily seen by ordinary standard techniques. The authors have brought together well written articles on the history, current developments, and possible directions for future research, which will be useful to both students and advanced researchers.” Professor Elliott H. Lieb Princeton University
Book Synopsis The Hubbard Model by : Dionys Baeriswyl
Download or read book The Hubbard Model written by Dionys Baeriswyl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).
Book Synopsis Exactly Solvable Models of Strongly Correlated Electrons by : Vladimir E. Korepin
Download or read book Exactly Solvable Models of Strongly Correlated Electrons written by Vladimir E. Korepin and published by World Scientific. This book was released on 1994 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-c superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.
Book Synopsis Quantum Electron Liquids and High-Tc Superconductivity by : Jose Gonzalez
Download or read book Quantum Electron Liquids and High-Tc Superconductivity written by Jose Gonzalez and published by Springer Science & Business Media. This book was released on 2008-11-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from a course given at the Univcrsidad Aut6noma of Madrid in the Spring of 1994 and in the Universidad Complutense of Madrid in 1995. 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-1~ superconducting materials. As theoretical physicists, our starting viewpoint to address the problem of strongly correlat ed ferlnion systems and related issues of modern condensed matter physics ·is the renormalization group approach applied both to quantU111 field theory and statistical physics. In recent years this has become not only a powerful tool for retrieving the essential physics of interacting systems but also a link between theoretical physics and modern condensed matter physics. Furthermore, once we have this common background for dealing with apparently different prob lems, we discuss more specific topics and even phenomenological aspects of the field. In doing so we have tried to make the exposition clear and simple, with out entering into technical details but focusing ill the fundamental physics of the phenomena under study. Therefore ,ve expect that our experience ll1ay have some value to other people entering this fascinating field. We have divided these notes into three parts and each part into chapters, which correspond roughly to one or two lectures. Part I, Chaps. 1-2 (A. H. V.
Book Synopsis Many-body Problem, The: An Encyclopedia Of Exactly Solved Models In One Dimension (3rd Printing With Revisions And Corrections) by : Daniel C Mattis
Download or read book Many-body Problem, The: An Encyclopedia Of Exactly Solved Models In One Dimension (3rd Printing With Revisions And Corrections) written by Daniel C Mattis and published by World Scientific. This book was released on 1993-03-15 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space — such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz — can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Book Synopsis The Quantum Hall Effect by : Daijiro Yoshioka
Download or read book The Quantum Hall Effect written by Daijiro Yoshioka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has opened up a new paradigm in the study of strongly correlated electrons and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. This book explains the quantum Hall effects together with these new concepts starting from elementary quantum mechanics.
Book Synopsis Polarons and Bipolarons by : Ashok Chatterjee
Download or read book Polarons and Bipolarons written by Ashok Chatterjee and published by CRC Press. This book was released on 2018-10-09 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive review of the subject of polaron and a thorough account of the sophisticated theories of the polaron. It explains the concept of the polaron physics in as simple a manner as possible and presents the theoretical techniques and mathematical derivations in great detail. Anybody who follows this book will develop a solid command over the subject both conceptually and technically and will be in a position to contribute to this field.
Book Synopsis Self-consistent Quantum-Field Theory and Bosonization for Strongly Correlated Electron Systems by : Rudolf Haussmann
Download or read book Self-consistent Quantum-Field Theory and Bosonization for Strongly Correlated Electron Systems written by Rudolf Haussmann and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Strong Interactions in Low Dimensions by : D. Baeriswyl
Download or read book Strong Interactions in Low Dimensions written by D. Baeriswyl and published by Springer Science & Business Media. This book was released on 2007-09-29 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an attempt to convey the colorful facets of condensed matter systems with reduced dimensionality. Some of the specific features predicted for interacting one-dimensional electron systems, such as charge- and spin-density waves, have been observed in many quasi-one-dimensional materials. The two-dimensional world is even richer: besides d-wave superconductivity and the Quantum Hall Effect - perhaps the most spectacular phases explored during the last two decades - many collective charge and spin states have captured the interest of researchers, such as charge stripes or spontaneously generated circulating currents. Recent years have witnessed important progress in material preparation, measurement techniques and theoretical methods. Today larger and better samples, higher flux for neutron beams, advanced light sources, better resolution in electron spectroscopy, new computational algorithms, and the development of field-theoretical approaches allow an in-depth analysis of the complex many-body behaviour of low-dimensional materials. The epoch when simple mean-field arguments were sufficient for describing the gross features observed experimentally is definitely over. The Editors' aim is to thoroughly explain a number of selected topics: the application of dynamical probes, such as neutron scattering, optical absorption and photoemission, as well as transport studies, both electrical and thermal. Some of the more theoretical chapters are directly relevant for experiments, such as optical spectroscopy, transport in one-dimensional models, and the phenomenology of charge inhomogeneities in layered materials, while others discuss more general topics and methods, for example the concept of a Luttinger liquid and bosonization, or duality transformations, both promising tools for treating strongly interacting many-body systems.
Download or read book Bosonization written by Michael Stone and published by World Scientific. This book was released on 1994-12-23 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bosonization is a useful technique for studying systems of interacting fermions in low dimensions. It has applications in both particle and condensed matter physics. This book contains reprints of papers on the method as used in these fields. The papers range from the classic work of Tomonaga in the 1950's on one-dimensional electron gases, through the discovery of fermionic solitons in the 1970's, to integrable systems and bosonization on Riemann surfaces. A four-chapter pedagogical introduction by the editor should make the book accessible to graduate students and experienced researchers alike. Contents: Remarks on Bloch's Method of Sound Waves Applied to Many Fermion Problems (S Tomonaga)Particle States of a Quantized Meson Field (T H R Skyrme)Soliton Operators for the Quantized Sine-Gordon Equation (S Mandelstam)Theory of Non-Abelian Goldstone Bosons in Two Dimensions (A M Polyakov & P Weigman)Non-Abelian Bosonization in Two Dimensions (E Witten)Chiral Bosonization, Determinants, and the String Partition Function (E Verlinde & H Verlinde)Bosonization on Higher Genus Riemann Surfaces (L Alvarez-Gaume et al.)Transformation Groups for Soliton Equations (E Date et al.)Coherent-State Path Integrals for Loop Groups and Non-Abelian Bosonization (M Stone)and other papers Readership: Students and researchers in high energy and condensed matter physics. keywords:
Book Synopsis Field Theories of Condensed Matter Physics by : Eduardo Fradkin
Download or read book Field Theories of Condensed Matter Physics written by Eduardo Fradkin and published by Cambridge University Press. This book was released on 2013-02-28 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Book Synopsis Condensed Matter Physics and Exactly Soluble Models by : Elliott H. Lieb
Download or read book Condensed Matter Physics and Exactly Soluble Models written by Elliott H. Lieb and published by Springer Science & Business Media. This book was released on 2004-11-29 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.
Book Synopsis Geometric Analysis and Applications to Quantum Field Theory by : Peter Bouwknegt
Download or read book Geometric Analysis and Applications to Quantum Field Theory written by Peter Bouwknegt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Book Synopsis The Recursion Method by : V.S. Viswanath
Download or read book The Recursion Method written by V.S. Viswanath and published by Springer Science & Business Media. This book was released on 2008-10-10 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the recursion method is presented as a method for the analysis of dynamical properties of quantum and classical many-body systems in thermal equilibrium. Such properties are probed by many different experimental techniques used in materials science. Several representations and formulations of the recursion method are described in detail and documented with numerous examples, ranging from elementary illustrations for tutorial purposes to realistic models of interest in current research in the areas of spin dynamics and low-dimensional magnetism. The performance of the recursion method is calibrated by exact results in a number of benchmark tests and compared with the performance of other calculational techniques. The book addresses graduate students and researchers.
Book Synopsis Quantum Many-Body Systems in One Dimension by : Zachary N C Ha
Download or read book Quantum Many-Body Systems in One Dimension written by Zachary N C Ha and published by World Scientific. This book was released on 1996-09-13 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the 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. Contents:IntroductionHeisenberg Spin ChainThe 1D Hubbard ModelModels with Inverse-Square ExchangeStrings in Long-Range Interaction ModelElementary Excitations of t-J ModelFractional Statistics in One-Dimension: View from an Exactly Solvable ModelConcluding Remarks Readership: Graduate students, researchers in statistical mechanics, mathematical physics and condensed matter physics. keywords:Quantum;Many-Body;One;Inverse Square;Exchange;Luttinger;Fractional Statistics
