It is found that a new two-dimensional (2D) lattice model of two coupled asymmetric six-vertex models provides a one-parameter family of transfer matrices commuting with the Hamiltonian of the 1D Hubbard model with a chemical potential term, for a special choice of the coupling constants. This new statistical model can be regarded as a four-state model in two dimensions, since the six-vertex model can be viewed as a two-state one. It is conjectured that this "covering" model satisfies the Yang-Baxter equations, i.e., it possesses a commuting family of row-to-row transfer matrices. Moreover, an alternative generating functional for an infinite number of conservation laws in the 1D Hubbard model is written down. This may be useful in understanding the completeness of the set of local conserved currents.
The 1D Hubbard model is shown to be an exactly integrable system. A "covering" model of 2D statistical mechanics which I proposed recently was shown to provide a one-parameter family of transfer matrices, commuting with the Hamiltonian of the Hubbard model. I show in this work that any two transfer matrices of a family commute mutually. At the root of the commutation relation is the ubiquitous Yang-Baxter factorization condition. The form of the
R operator is displayed explicitly.
We examine the nature, number, and interrelation of conservation laws in the one-dimensional Hubbard model. In previous work by Shastry [Phys. Rev. Lett. 56, 1529 (1986); 56, 2334 (1986); 56, 2453 (1986); J. Stat. Phys. 50, 57 (1988)], who studied the model on a large but finite number of lattice sites
(Na), only
Na+1 conservation laws, corresponding to
Na+1 operators that commute with themselves and the Hamiltonian, were explicitly identified, rather than the $\ensuremath{\sim}{2N}_{a}$ conservation laws expected from the solvability and integrability of the model. Using a pseudoparticle approach related to the thermodynamic Bethe ansatz, we discover an additional
Na+1 independent conservation laws corresponding to nonlocal, mututally commuting operators, which we call transfer-matrix currents. Further, for the model defined in the whole Hilbert space, we find there are two other independent commuting operators (the squares of the \ensuremath{\eta}-spin and spin operators) so that the total number of local plus nonlocal commuting conservation laws for the one-dimensional Hubbard model is
2Na+4. Finally, we introduce an alternative set of
2Na+4 conservation laws which assume particularly simple forms in terms of the pseudoparticle and Yang-particle operators. This set of mutually commuting operators lends itself more readily to calculations of physically relevant correlation functions at finite energy or frequency than the previous set.
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.