The Lax pair formulation is presented for completely integrable quantum lattice spin open chains. Specifically, the Lax pair for the one-dimensional Heisenberg XXZ open chain is explicitly constructed. Our construction provides an alternative and direct demonstration of the quantum integrability of the system.
The Lax pair for the one-dimensional Hubbard spin chain with open boundary conditions (BC) is explicitly constructed and two different kinds of boundary K-matrices compatible with the integrability of the model are obtained. Our construction provides an alternative and direct demonstration for the quantum integrability of the model and it is found that the model is related to a class of commuting transfer matrices of an equivalent coupled asymmetric six-vertex model with open BC. Our results show that the chemical potential term is indeed nontrivial for the underlying algebraic structure of the model.