Topics of solvable lattice models and conformal field theories
Several topics (spin chains, Bethe Ansatz, Gaudin models, WZW models and their relations etc.) in the theory of solvable lattice models and conformal field theories are discussed. Knowledge on quantum mechanics and statistical mechanics will help understanding but it is not indispensable, as we shall start from the very short review on them and put emphasis on mathematical aspects. We mainly focus on so-called "rational models", but if time permits, "elliptic models" might be discussed.
Lecturer
Date
15th September, 2026 ~ 5th January, 2027
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 14:20 - 16:55 | Shuangqing | - | - | - |
Prerequisite
Linear algebra, complex analysis. Knowledge on physics is welcome, but not indispensable.
Syllabus
We shall discuss following topics, but not strictly constrained to this list.
1. Review on quantum mechanics
2. Spin chain
3. Review of classical statistical mechanics
4. Vertex model and transfer matrix
5. 6-vertex models and spin chan models
6. Bethe Ansatz for the XXX model
7. Gaudin model
8. WZW model.
9. Critical level limit of WZW model and Gaudin model.
10. Wakimoto modules and Bethe Ansatz.
11. Reviews of elliptic functions.
12. The XYZ spin chain, the 8-vertex model and their Bethe Ansatz.
1. Review on quantum mechanics
2. Spin chain
3. Review of classical statistical mechanics
4. Vertex model and transfer matrix
5. 6-vertex models and spin chan models
6. Bethe Ansatz for the XXX model
7. Gaudin model
8. WZW model.
9. Critical level limit of WZW model and Gaudin model.
10. Wakimoto modules and Bethe Ansatz.
11. Reviews of elliptic functions.
12. The XYZ spin chain, the 8-vertex model and their Bethe Ansatz.
Reference
R. J. Baxter: Exactly solved models in statistical mechanics.
B.Feigin, E.Frenkel, N.Reshetikhin: Gaudin model, Bethe Ansatz and critical level, Comm. Math. Phys. 166 (1994), 27–62.
Jimbo, Michio; Miwa, Tetsuji: Algebraic analysis of solvable lattice models. CBMS Regional Conference Series in Mathematics, 85. American Mathematical Society, (1995).
L. A. Takhtajan, L.D. Faddeev: The quantum method of the inverse problem and the Heisenberg XYZ model, Uspekhi Mat. Nauk 34:5 (1979), 13–63, (in Russian); Russian Math. Surveys 34:5 (1979), 11–68, (English transl.).
B.Feigin, E.Frenkel, N.Reshetikhin: Gaudin model, Bethe Ansatz and critical level, Comm. Math. Phys. 166 (1994), 27–62.
Jimbo, Michio; Miwa, Tetsuji: Algebraic analysis of solvable lattice models. CBMS Regional Conference Series in Mathematics, 85. American Mathematical Society, (1995).
L. A. Takhtajan, L.D. Faddeev: The quantum method of the inverse problem and the Heisenberg XYZ model, Uspekhi Mat. Nauk 34:5 (1979), 13–63, (in Russian); Russian Math. Surveys 34:5 (1979), 11–68, (English transl.).
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Takashi Takebe is a researcher of mathematical physics, in particular integrable systems. He worked as a professor at the faculty of mathematics of National Research University Higher School of Economics in Moscow, Russia, till August 2023 and joined BIMSA as a professor in September 2023.