Integrable perturbation of Yang-Lee model
Pythagoras0 (토론 | 기여)님의 2020년 11월 16일 (월) 10:49 판
introduction
- S-matrix describes the infrared data of the model
- it is important to check that the UV limit of the model coincides with the conformal field theory that was originally perturbed
- TBA is a method which provides such a check
perturbed action
- $\mathcal{A}_{SLYM}=\mathcal{A}_{M_{2,5}}+i \lambda \int d^2x \varphi(x)$
- $M=(2.642944662\cdots) \lambda^{5/12}$ where $M$ is the single particle mass
- http://www.wolframalpha.com/input/?i=2.642944662
- spin of conserved charges : 1,5,7,11,13,17,19, ...
S-matrix
- 1 particle
- S-matrix
$$ S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right) $$
- 커널
$$ \phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right) $$
TBA analysis
$$ N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1 $$
- Integrable perturbations of Ising model
- (2,5) minimal Yang-Lee model
- Massive integrable perturbations of CFT and quasi-particles
computational resource
articles
- Bianchini, Davide, Olalla A. Castro-Alvaredo, and Benjamin Doyon. ‘Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory’. arXiv:1502.03275 [cond-Mat, Physics:hep-Th], 11 February 2015. http://arxiv.org/abs/1502.03275.
- Fateev, V. A. 1994. “The Exact Relations Between the Coupling Constants and the Masses of Particles for the Integrable Perturbed Conformal Field Theories.” Physics Letters. B 324 (1): 45–51. doi:10.1016/0370-2693(94)00078-6. http://www.sciencedirect.com/science/article/pii/0370269394000786
- Zamolodchikov, Al.B. 1990. “Thermodynamic Bethe Ansatz in Relativistic Models: Scaling 3-state Potts and Lee-Yang Models.” Nuclear Physics B 342 (3) (October 8): 695–720. doi:10.1016/0550-3213(90)90333-9. http://www.sciencedirect.com/science/article/pii/0550321390903339
- Cardy, John L., and G. Mussardo. 1989. “S-matrix of the Yang-Lee Edge Singularity in Two Dimensions.” Physics Letters B 225 (3) (July 20): 275–278. doi:10.1016/0370-2693(89)90818-6. http://www.sciencedirect.com/science/article/pii/0370269389908186