Quantum integrable spin chains
In our course, we will study integrable structures based on quantum algebras.
We will examine the Yang-Baxter equations as the foundation of quantum integrability
and the Bethe ansatz as the primary method for solving them.
The second half of the course is dedicated to studying the form-factor approach to correlation functions.
We will examine the Yang-Baxter equations as the foundation of quantum integrability
and the Bethe ansatz as the primary method for solving them.
The second half of the course is dedicated to studying the form-factor approach to correlation functions.
Lecturer
Date
16th March ~ 7th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday,Thursday | 10:40 - 12:15 | A3-2-303 | ZOOM 12 | 815 762 8413 | BIMSA |
Prerequisite
The knowledge of linear algebra and basic methods of analysis (integral calculus, theory of the function of a complex variable, determinant identities) is required. The knowledge of representation theory of sl_2 is welcome. The familiarity with the basics of quantum mechanics(Hamiltonian, wavefunctions, Pauli matrices) will be useful throughout the whole course.
Syllabus
This course roughly splits into two parts.
In the first part, we will study the methods of quantum integrable systems using the Heisenberg spin chain as an example.
In the second part, we will study the thermodynamic limit, focusing on form-factors and correlation functions.
We will mainly be following Slavnov's lectures on "Algebraic Bethe ansatz".
In the first part, we will study the methods of quantum integrable systems using the Heisenberg spin chain as an example.
In the second part, we will study the thermodynamic limit, focusing on form-factors and correlation functions.
We will mainly be following Slavnov's lectures on "Algebraic Bethe ansatz".
Reference
* Lectures
N. A. Slavnov "Algebraic Bethe ansatz" https://arxiv.org/abs/1804.07350
N. Reshetikhin "Lectures on the integrability of the 6-vertex model" https://arxiv.org/abs/1010.5031.pdf
L. D. Faddeev "How Algebraic Bethe Ansatz works for integrable model" https://arxiv.org/pdf/hep-th/9605187.pdf
* Books
R. J. Baxter, Exactly solved models in statistical mechanics (1982)
M. Gaudin, The Bethe wavefunction. (1983 in French, 2014 in English)
V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions. (1993)
N. A. Slavnov "Algebraic Bethe ansatz" https://arxiv.org/abs/1804.07350
N. Reshetikhin "Lectures on the integrability of the 6-vertex model" https://arxiv.org/abs/1010.5031.pdf
L. D. Faddeev "How Algebraic Bethe Ansatz works for integrable model" https://arxiv.org/pdf/hep-th/9605187.pdf
* Books
R. J. Baxter, Exactly solved models in statistical mechanics (1982)
M. Gaudin, The Bethe wavefunction. (1983 in French, 2014 in English)
V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions. (1993)
Audience
Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Andrii Liashyk is a researcher in the field of integrated systems, mainly quantum ones. He received his degree from the Center for Advanced Study at Skoltech in 2020. In 2022 he joined BIMSA as a Assistant Professor.