On the solutions to the multi-parametric Yang–Baxter equations

Abstract

A unified approach is applied in the consideration of the multi-parametric (colored) Yang-Baxter equations (YBE) and the usual YBE with two-parametric R-matrices, relying on the existence of the arbitrary functions in the general solutions. The colored YBE are considered with the R-matrices defined on two and three dimensional states. We present an exhaustive study and the overall solutions for the YBE with 4 × 4 colored R-matrices. The established classification includes new multi-parametric free fermionic solutions. In the context of the given approach there are obtained the colored solutions to the YBE with 9 × 9 R-matrices having 15 non-zero elements.

Yang-Baxter and the Boost: splitting the difference

“…Next we apply our method to R-matrices of size 9 × 9 corresponding to local Hilbert spaces of dimension 3. In the literature there are many examples of such models including [14, 39, 45-47, 50-52, [63][64][65][66].…”

“…We complete the classification of fifteen-vertex models developed in [39,64]. As a result of the Cartan symmetry we consider a Hamiltonian density of the form…”

“…In our approach the solutions obtained in[64] are of difference form, in the sense that be mapped to difference form by a twist.…”

Yang-Baxter and the Boost: splitting the difference

“…Next we apply our method to R-matrices of size 9 × 9 corresponding to local Hilbert spaces of dimension 3. In the literature there are many examples of such models including [9,19,24,25,27,[34][35][36][37].…”

“…We complete the classification of fifteen-vertex models developed in [19,35]. As a result of the Cartan symmetry we consider a Hamiltonian density of the form…”