Yang—Baxter Relation

Michio Kaku

Eugenio Olmedilla, Miki Wadati, Yasuhiro Akutsu

A systematic method to derive the Yang-Baxter relations for the fermion models which are equivalent to the solvable spin models is presented. The method is applied to prove the Yang-Baxter relation and the commutability of the transfer matrices for the one-dimensional Hubbard model.

Miki Wadati, Kiyoshi Sogo, M. Uchinami +1 more

Masao Nomura

Relations are exploited among Clebsch–Gordan (CG) and Racah coefficients in the algebra suq(2), known as a deformation of su(2). These are used to show that the Yang–Baxter (YB) relation for the IRF (interaction round a face) model results from one of the symmetry relations for the 9-j symbol specific to suq(2), and that in an asymptotic limit this YB relation becomes the YB relation for the two-dimensional vertex model. The Racah coefficient, which has a particularly simple dependence on q, is efficiently used such that an asymptotic limit of the Racah coefficient is the CG coefficient and another limit gives the factorized S matrix of the vertex model.

三樹 和達, 清 十河, 守 打波 +1 more

Kiyoshi Sogo, M. Uchinami, Yuko Akutsu +1 more

In the case of two-component models, all possible solutions for factorization equations of S-matrix are obtained. These solutions give a classification of solvable vertex models. It is found that Yang-Baxter relation is more general than the factorization equation. The six vertex model by Yang, Yang and Sutherland is derived not from the factorization equation but from Yang-Baxter relation. Thus it is concluded that Yang-Baxter relation lies at the basis of all the known solvable two component models. Furthermore, spin Hamiltonians corresponding to our vertex models are presented in explicit forms.