Exact integrability of the one-dimensional Hubbard model.

We have recently shown (]) that the one-dimensional ( ld) Hubbard model possesses an infinite number of conservation laws by identifying a 2d classical statistical model for which a one-parameter family of transfer matrices commutes with the Hamiltonian. Reference2 contains a demonstrat ion that the one-parameter family of transfer matrices commute mutually and hence we have a new completely integrable problem. This embedding of the ld Hubbard model into a covering 2d statistical model parallels the well-known relationship between the ld X Y Z model and the 2d eight-vertex models established by Sutherland and Baxter. (3'4) In this paper we present some further results on the covering statistical model, and also recover the previous results of Refs. 1 and 2 through a promising new line of argument. The eigenfunctions of the ld Hubbard model were found by Lieb and Wu (5) using the Bethe-Yang or nested Bethe Ansatz technique. The