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Author : Alexander Altland
ISBN : 9780521769754
Genre : Science
File Size : 47.42 MB
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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

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.

Why is quantum field theory of condensed matter physics necessary? Condensed matter physics deals with a wide variety of topics, ranging from gas to liquids and solids, as well as plasma, where owing to the inter play between the motions of a tremendous number of electrons and nuclei, rich varieties of physical phenomena occur. Quantum field theory is the most appropriate "language", to describe systems with such a large number of de grees of freedom, and therefore its importance for condensed matter physics is obvious. Indeed, up to now, quantum field theory has been succesfully ap plied to many different topics in condensed matter physics. Recently, quan tum field theory has become more and more important in research on the electronic properties of condensed systems, which is the main topic of the present volume. Up to now, the motion of electrons in solids has been successfully de scribed by focusing on one electron and replacing the Coulomb interaction of all the other electrons by a mean field potential. This method is called mean field theory, which made important contributions to the explanantion of the electronic structure in solids, and led to the classification of insulators, semiconductors and metals in terms of the band theory. It might be said that also the present achievements in the field of semiconductor technology rely on these foundations. In the mean field approximation, effects that arise due to the correlation of the motions of many particles, cannot be described.

Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm–Pines and Chern–Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.

Author : Eduardo C. Marino
ISBN : 9781107074118
Genre : Science
File Size : 64.56 MB
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Independent electrons and static crystals -- Vibrating crystals -- Interacting electrons -- Interactions in action -- Functional formulation of quantum field theory -- Quantum fields in action -- Symmetries: explicit or secret -- Classical topological excitations -- Quantum topological excitations -- Duality, bosonization and generalized statistics -- Statistical transmutation -- Pseudo quantum electrodynamics -- Quantum field theory methods in condensed matter -- Metals, Fermi liquids, Mott and Anderson insulators -- The dynamics of polarons -- Polyacetylene -- The Kondo effect -- Quantum magnets in 1D: Fermionization, bosonization, Coulomb gases and 'all that' -- Quantum magnets in 2D: nonlinear sigma model, CP1 and 'all that' -- The spin-fermion system: a quantum field theory approach -- The spin glass -- Quantum field theory approach to superfluidity -- Quantum field theory approach to superconductivity -- The cuprate high-temperature superconductors -- The pnictides: iron based superconductors -- The quantum Hall effect -- Graphene -- Silicene and transition metal dichalcogenides -- Topological insulators -- Non-abelian statistics and quantum computation

Author : Christopher Mudry
ISBN : 9789814449120
Genre : Science
File Size : 59.86 MB
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The aim of this book is to introduce a graduate student to selected concepts in condensed matter physics for which the language of field theory is ideally suited. The examples considered in this book are those of superfluidity for weakly interacting bosons, collinear magnetism, and superconductivity. Quantum phase transitions are also treated in the context of quantum dissipative junctions and interacting fermions constrained to one-dimensional position space. The style of presentation is sufficiently detailed and comprehensive that it only presumes familiarity with undergraduate physics.

Author : Hendrik B. Geyer
ISBN : 3540601384
Genre : Mathematics
File Size : 81.13 MB
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This topical volume contains five pedagogically written articles on the interplay between field theory and condensed matter physics. The main emphasis is on the topological aspects, and especially quantum Hall fluids, and superconductivity is treated extensively. Other topics are conformal invariance and path integrals. The articles are carefully edited so that the book could ideally serve as a text for special graduate courses.

This book is a pedagogical and systematic introduction to new concepts and quantum field theoretical methods in condensed matter physics, which may have an impact on our understanding of the origin of light, electrons and other elementary particles in the universe. Emphasis is on clear physical principles, while at the same time bringing students to the fore of today's research.

In this book the author extends the concepts introduced in his Quantum Field Theory in Condensed Matter Physics to situations in which the strong electronic correlations are crucial for the understanding of the observed phenomena. Starting from a model field theory to illustrate the basic ideas, more complex systems are analyzed in turn. A special chapter is devoted to the description of antiferromagnets, doped Mott insulators, and quantum Hall liquids from the point of view of gauge theory.

Author : Adriaan M J Schakel
ISBN : 9789813107199
Genre : Science
File Size : 23.94 MB
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This textbook covers the main topics in contemporary condensed matter physics in a modern and unified way, using quantum field theory in the functional-integral approach. The book highlights symmetry aspects in acknowledging that much of the collective behaviors of condensed matter systems at low temperatures emerge above a nontrivial ground state, which spontaneously breaks the symmetry. The emphasis is on effective field theories which provide an efficient and powerful description that is valid at long wavelengths and low frequencies. In conjunction with the emphasis on effective theories, a modern approach towards renormalization is taken, whereby a wavenumber cut-off is introduced to set a scale beyond which the microscopic model under consideration ceases to be valid. The unique and innovative character of this presentation, free of historical constraints, allows for a compact and self-contained treatment of the main topics in contemporary condensed matter physics.