qKZ and Bethe ansatz
We will look at how the quantum Knizhnik-Zamolodchikov (qKZ) equation arises in the study of quantum integrable systems and how quantum spin chains help to solve the qKZ equation.
In the course we will cover the KZ equation and its quantum analogue. On the side of integrable systems we will study the Heisenberg spin chains and Gaudin models.
In the first half of the course, we will consider the case of gl(2). In the second part, we will consider the generalisation to the case of gl(n).
In the course we will cover the KZ equation and its quantum analogue. On the side of integrable systems we will study the Heisenberg spin chains and Gaudin models.
In the first half of the course, we will consider the case of gl(2). In the second part, we will consider the generalisation to the case of gl(n).
讲师
日期
2025年03月04日 至 05月30日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周五 | 13:30 - 15:05 | A3-2-303 | ZOOM 11 | 435 529 7909 | BIMSA |
修课要求
Linear algebra and other standard courses of the first two years of a mathematics or physics department. Basics of Lie algebra and its representation theory.
课程大纲
- Introduction to spin chain and solution of XXX Heisenberg spin chain using Bethe ansatz.
[Z] section 2.1, [S] sections 1, 4.
- Spin chain and relation to vertex models
[Z] section 3.1, 3.2, [S] section 1.2, section 6
[Z] section 2.1, [S] sections 1, 4.
- Spin chain and relation to vertex models
[Z] section 3.1, 3.2, [S] section 1.2, section 6
参考资料
[Z] A. Zabrodin, "Lectures on Bethe ansatz and quantum integrable systems", http://crei.skoltech.ru/app/data/uploads/sites/42/2023/04/backint3.pdf
[S] N. Slavnov, "Algebraic Bethe ansatz", https://arxiv.org/pdf/1804.07350
M. Jimbo and T, Miwa, "Algebraic Analysis of Solvable Lattice Models"
H. M. Babujian and R. Flume, "Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations"
P. I. Etingof, I. Frenkel, A. A. Kirillov, Lectures on Representation Theory and Knizhnik–Zamolodchikov Equations
V. Tarasov, A. Varchenko "Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation", https://arxiv.org/abs/hep-th/9311040
V. Tarasov, A. Varchenko "Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz", https://arxiv.org/abs/hep-th/9411181
[S] N. Slavnov, "Algebraic Bethe ansatz", https://arxiv.org/pdf/1804.07350
M. Jimbo and T, Miwa, "Algebraic Analysis of Solvable Lattice Models"
H. M. Babujian and R. Flume, "Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations"
P. I. Etingof, I. Frenkel, A. A. Kirillov, Lectures on Representation Theory and Knizhnik–Zamolodchikov Equations
V. Tarasov, A. Varchenko "Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation", https://arxiv.org/abs/hep-th/9311040
V. Tarasov, A. Varchenko "Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz", https://arxiv.org/abs/hep-th/9411181
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。