EAN: 9783319484860

AN INTRODUCTION TO INTEGRABLE TECHNIQUES FOR ON...

This book introduces the reader to basic notions of integrable techniques for one-dimensional
quantum systems. In a pedagogical way  a few examples of exactly solvable models are worked out
to go from the coordinate approach to the Algebraic Bethe Ansatz  with some discussion on the
finite temperature thermodynamics. 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 into the 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.

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