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Lecture Notes in Physics

Quantum Spin Systems on Infinite Lattices

A Concise Introduction

Authors: Naaijkens, Pieter

  • 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
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-51458-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-51456-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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 allows ideas 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.  

Reviews

“The book, which arose from the lectures given by the author to a mathematical physics-oriented audience, is a concise ... introduction to methods of quantum physics and basic mathematical inventory (technical tools) appropriate for the study of infinite quantum spin 1/2 systems. ... provides a background and pointers for the reader, to start on his/her own the exploration of the recent literature on the operator algebra approach to quantum many-body systems.” (Piotr Garbaczewski, zbMATH 1375.82002, 2018)


Table of contents (6 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-51458-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-51456-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Spin Systems on Infinite Lattices
Book Subtitle
A Concise Introduction
Authors
Series Title
Lecture Notes in Physics
Series Volume
933
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-51458-1
DOI
10.1007/978-3-319-51458-1
Softcover ISBN
978-3-319-51456-7
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XI, 177
Number of Illustrations
5 b/w illustrations, 1 illustrations in colour
Topics