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.
讲师
日期
2026年03月16日 至 06月07日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三,周四 | 10:40 - 12:15 | A3-2-303 | ZOOM 12 | 815 762 8413 | BIMSA |
修课要求
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.
课程大纲
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".
参考资料
* 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)
听众
Advanced Undergraduate
, Graduate
, 博士后
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Andrii Liashyk的研究领域是可积系统，主要研究量子系统。他于2020年获得了Skoltech高等研究中心的博士学位。2022年，他加入BIMSA担任助理教授。