An Introduction To Integrable Techniques For One-dimensional Quantum Systems (lecture Notes In Physics)
by Fabio Franchini /
2017 / English / PDF
2.9 MB Download
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.
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.
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.