"Bethe ansatz for RSOS models"의 두 판 사이의 차이
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| 5번째 줄: | 5번째 줄: | ||
==TBA equation== | ==TBA equation== | ||
* taken from [[T-systems and Y-systems in integrable systems]] | * taken from [[T-systems and Y-systems in integrable systems]] | ||
| − | * RSOS model associated with the representation | + | * RSOS model associated with the representation <math>W_{s}^{(p)}</math> of <math>U_q(\hat{\mathfrak{g}})</math>. |
| − | * | + | * <math>N</math> : length of sites |
| − | * | + | * <math>C=(C_{ab})</math> : Cartan matrix |
| − | * | + | * <math>L=\ell +h^{\vee}</math> |
The Bethe equation is the following | The Bethe equation is the following | ||
for the unknowns | for the unknowns | ||
| − | + | <math>\{u^{(a)}_j \vert \, a \in I, 1 \le j \le n_a \}</math>: | |
\begin{equation}\label{ber} | \begin{equation}\label{ber} | ||
| 25번째 줄: | 25번째 줄: | ||
u^{(a)}_j - u^{(b)}_k + \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}. | u^{(a)}_j - u^{(b)}_k + \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}. | ||
\end{equation} | \end{equation} | ||
| − | Here | + | Here <math>n_a=Ns(C^{-1})_{a p}</math> as in (3.51) |
| − | with | + | with <math>(r_i,s_i)=(p,s)</math> for all <math>i</math>, and |
| − | + | <math>\Omega_a</math> is a root of unity | |
2020년 11월 16일 (월) 05:31 기준 최신판
introduction
- see chapter 15 of T-systems and Y-systems in integrable systems for basics
TBA equation
- taken from T-systems and Y-systems in integrable systems
- RSOS model associated with the representation \(W_{s}^{(p)}\) of \(U_q(\hat{\mathfrak{g}})\).
- \(N\) : length of sites
- \(C=(C_{ab})\) : Cartan matrix
- \(L=\ell +h^{\vee}\)
The Bethe equation is the following for the unknowns \(\{u^{(a)}_j \vert \, a \in I, 1 \le j \le n_a \}\):
\begin{equation}\label{ber} \Biggl(\frac{\sinh{\pi\over 2L}\bigl( u^{(a)}_j - \sqrt{-1}{s \over t_p}\delta_{a p}\bigr)} {\sinh{\pi\over 2L}\bigl( u^{(a)}_j + \sqrt{-1}{s \over t_p}\delta_{a p}\bigr)} \Biggr)^N = \Omega_a \prod_{b=1}^r\prod_{k=1}^{n_b} \frac{\sinh{\pi\over 2L}\bigl( u^{(a)}_j - u^{(b)}_k - \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)} {\sinh{\pi\over 2L}\bigl( u^{(a)}_j - u^{(b)}_k + \sqrt{-1}(\alpha_a \vert \alpha_b)\bigr)}. \end{equation} Here \(n_a=Ns(C^{-1})_{a p}\) as in (3.51) with \((r_i,s_i)=(p,s)\) for all \(i\), and \(\Omega_a\) is a root of unity
articles
- Babichenko, A. 2004. “From S-matrices to the Thermodynamic Bethe Ansatz.” Nuclear Physics B 697 (3) (October 11): 481–512. doi:10.1016/j.nuclphysb.2004.07.008.
- Dasmahapatra, Srinandan. 1993. “String Hypothesis and Characters of Coset CFTs”. ArXiv e-print hep-th/9305024. http://arxiv.org/abs/hep-th/9305024.
- Kuniba, A. (1993). Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity. Nuclear Physics B, 389(1), 209–244. doi:10.1016/0550-3213(93)90291-V
- Bazhanov, V. V., and N. Reshetikhin. 1990. “Restricted Solid-on-solid Models Connected with Simply Laced Algebras and Conformal Field Theory.” Journal of Physics A: Mathematical and General 23 (9) (May 7): 1477. doi:10.1088/0305-4470/23/9/012.
- Bazhanov, V. V., and N. Yu. Reshetikhin. 1989. “Critical RSOS Models and Conformal Field Theory.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 4 (1): 115–142. doi:10.1142/S0217751X89000042.
- Reshetikhin, N.Yu., and P.B. Weigmann. 1987. “Towards the Classification of Completely Integrable Quantum Field Theories (the Bethe-Ansatz Associated with Dynkin Diagrams and Their Automorphisms).” Physics Letters B 189 (1–2) (April 30): 125–131. doi:10.1016/0370-2693(87)91282-2.
- Reshetikhin, N. Yu. 1987. “The Spectrum of the Transfer Matrices Connected with Kac-Moody Algebras.” Letters in Mathematical Physics 14 (3) (October 1): 235–246. doi:10.1007/BF00416853.