  We explore the algebraic structure of a particular ansatz of Yang Baxter
Equation which is inspired from the Bethe Ansatz treatment of the ASEP
spin-model. Various classes of Hamiltonian density arriving from two types of
R-Matrices are found which also appear as solutions of constant YBE. We
identify the idempotent and nilpotent categories of such constant R-Matrices
and perform a rank-1 numerical search for the lowest dimension. A summary of
finalised results reveals general non-hermitian spin-1/2 chain models.
