Authors:
- Tutorially exposes an approach only treated in advanced monographs not very accessible to beginners
- Suitable both as textbook and as self-study guide
- Course-based primer which allows for entering the field quickly and efficiently
Part of the book series: Lecture Notes in Physics (LNP, volume 933)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
This course-based primer offers readers a concise introduction to the description of quantum mechanical systems with infinitely many degrees of freedom – and quantum spin systems in particular – using the operator algebraic approach. Here, the observables are modeled using elements of some operator algebra, usually a C*-algebra. This text introduces readers to the framework and the necessary mathematical tools without assuming much mathematical background, making it more accessible than advanced monographs.
The book also highlights the usefulness of the so-called thermodynamic limit of quantum spin systems, which is the limit of infinite system size. For example, this makes it possible to clearly distinguish between local and global properties, without having to keep track of the system size. Together with Lieb-Robinson bounds, which play a similar role in quantum spin systems to that of the speed of light in relativistic theories, this approach allowsideas from relativistic field theories to be implemented in a quantum spin system. Several related cases are discussed, demonstrating the merits of the operator algebraic approach.
Featuring representative worked-out examples and many exercises, this text is primarily targeted at graduate students and advanced undergraduates in theoretical physics or mathematics with a keen interest in mathematical physics. The material provides the necessary background and pointers to start exploring the recent literature. As such, it will also be useful for active researchers seeking a quick and comparatively self-contained introduction to the operator algebraic approach to quantum spin systems.
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Authors and Affiliations
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Department of Mathematics, University of California, Davis, USA
Pieter Naaijkens
Bibliographic Information
Book Title: Quantum Spin Systems on Infinite Lattices
Book Subtitle: A Concise Introduction
Authors: Pieter Naaijkens
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-51458-1
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-51456-7Published: 21 March 2017
eBook ISBN: 978-3-319-51458-1Published: 20 March 2017
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XI, 177
Number of Illustrations: 5 b/w illustrations, 1 illustrations in colour
Topics: Quantum Physics, Mathematical Physics, Mathematical Methods in Physics, Mathematical Applications in the Physical Sciences