Yang–Baxter equations and quantum entanglements

Abstract

In this paper some results associated with a new type of Yang---Baxter equation (YBE) are reviewed. The braiding matrix of Kauffman---Lomonaco has been extended to the solution (called type-II) of Yang---Baxter equation (YBE) and the related chain Hamiltonian is given. The Lorentz additivity for spectral parameters is found, rather than the Galilean rule for the familiar solutions (called type-I) of YBE associated with the usually exact solvable models. Based on the topological basis, the N-dimensional solution of YBE is found to be the Wigner D-functions. The explicit examples for spin-$$\frac{1}{2}$$12 and spin-1 have been shown. The extremes of $$\ell _1$$l1-norm of $$D$$D-functions are introduced to distinguish the type-I from type-II of braiding matrices that also correspond to those of von Neumann entropy for quantum information.