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Table of contents (5 chapters)
-
Front Matter
-
Back Matter
Keywords
- Lieb-Liniger model
- Heisenberg chain
- Yang-Baxter equations
- Toeplitz determinants
- bosonization
- XY chain
- XXZ chain
- Kitaev chain
- Bethe Ansatz
- Yan-Yang equation
- Inverse scattering problem
- Lax Representation
- Braid Limit
- Quantum Groups
- Strong Szegö theorem
- Widom's Theorem
- Fisher-Hartwig Conjecture
- Basor-Tracy Conjecture
- Slavnov's formulas
- Gaudin's formulas
About this book
The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped intothe corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Reviews
“This lecture note is a good source to learn basic notions and techniques of one-dimensional integrable quantum systems.” (Wencai Liu, zbMATH 1376.82001, 2018)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Introduction to Integrable Techniques for One-Dimensional Quantum Systems
Authors: Fabio Franchini
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-48487-7
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-48486-0Published: 26 May 2017
eBook ISBN: 978-3-319-48487-7Published: 25 May 2017
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XII, 180
Number of Illustrations: 6 b/w illustrations, 11 illustrations in colour
Topics: Mathematical Methods in Physics, Mathematical Physics, Condensed Matter Physics, Algebraic Geometry