Synopsis
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
Review
"While there are numerous research monographs..., a simple text introducing budding researchers to the fertile methods has been lacking. Professor Auerbach's book has been designed to fill this niche, and it is largely successful in this objective... An excellent feature is a set of exercises at the end of nearly every chapter, which not only lead the student through some of the mathematical steps left out of the text, but also addresses the ramifications of the concepts.... Auerbach's book is an excellent textbook for graduate students starting research in condensed matter theory, and captures well the excitement and creative ferment of the field in recent times. The student who peruses this book with care will be rewarded with a firm grasp of several current techniques, and the discrimination necessary to apply them with sophistication" -- Fndns. of Physics
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