Overview
- Provides the first comprehensive and detailed review of the Haldane phenomenon, a typical example of the “topological phase of matter,” and the subject of the 2016 Nobel Prize in Physics
- Discusses some of the most important universal properties of quantum many-body systems, which can be observed in a broad range of physical systems
- Begins with a pedagogical presentation of the necessary background information and leads the reader to subjects of active research, such as topological phases of matter
- Detailed and self-contained; all important results are carefully proved, using only undergraduate mathematics
- Provides a bridge between researchers in various fields, including condensed matter physics, high-energy physics, quantum information science, and mathematics
Part of the book series: Graduate Texts in Physics (GTP)
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Table of contents (11 chapters)
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Front Matter
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Long-Range Order and Spontaneous Symmetry Breaking
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Front Matter
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Haldane Phenomena and Beyond
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Front Matter
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Hubbard Model and the Origin of Magnetism
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Front Matter
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Back Matter
Keywords
About this book
This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter.
The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems.
The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Physics and Mathematics of Quantum Many-Body Systems
Authors: Hal Tasaki
Series Title: Graduate Texts in Physics
DOI: https://doi.org/10.1007/978-3-030-41265-4
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-41264-7Published: 08 May 2020
eBook ISBN: 978-3-030-41265-4Published: 07 May 2020
Series ISSN: 1868-4513
Series E-ISSN: 1868-4521
Edition Number: 1
Number of Pages: XVIII, 525
Number of Illustrations: 245 b/w illustrations, 2 illustrations in colour
Topics: Strongly Correlated Systems, Superconductivity, Mathematical Physics, Statistical Physics and Dynamical Systems, Phase Transitions and Multiphase Systems, Mathematical Methods in Physics