BIMSA

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.

2026年03月18日至 06月04日

Weekday	Time	Venue	Online	ID	Password
周三,周四	10:40 - 12:15	A3-2-303	ZOOM 12	815 762 8413	BIMSA

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.

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".

* Lecture 1 - XXX Heisenberg spin chain
In this lecture, we will formulate and solve the Heisenberg model.
By solution, we mean the algebraic equations that describe the model's eigenvalues and eigenfunctions.

References:
- A. Zabrodin "Lectures on Bethe ansatz and quantum integrable systems" Chapters 2.1.1
- N. A. Slavnov "Algebraic Bethe ansatz" Chapters 1.1-1.2

* Lecture 2-3 - XXX Heisenberg spin chain and its solution(coordinate Bethe ansatz)
In this lecture, we will formulate and solve the Heisenberg model.
By solution, we mean the algebraic equations that describe the model's eigenvalues and eigenfunctions.

References:
- H. Bethe "Zur Theorie der MetaUe. I. Eigenwerte und Eigenfunktionen der linearen Atomkette."
- A. Zabrodin "Lectures on Bethe ansatz and quantum integrable systems" Chapters 2.1.2-2.1.3

* 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
A. Zabrodin "Lectures on Bethe ansatz and quantum integrable systems" https://crei.skoltech.ru/app/data/uploads/sites/42/2023/04/backint3.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)

* Papers
- H. Bethe "Zur Theorie der MetaUe. I. Eigenwerte und Eigenfunktionen der linearen Atomkette." (1931)

Advanced Undergraduate , Graduate , 博士后

公开

英文

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。