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.
We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.
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.