Conservation laws in the one-dimensional Hubbard model - art. no. 205114

We examine the nature, number, and interrelation of conservation laws in th e one-dimensional Hubbard model. In previous work by Shastry [Phys. Rev. Le tt. 56, 1529 (1986); 56, 2334 (1986); 56, 2453 (1986); J. Stat. Phys. 50, 5 7 (1988)], who studied the model on a large but finite number of lattice si tes (N-a), only N-a + 1 conservation laws, corresponding to N-a + 1 operato rs that commute with themselves and the Hamiltonian, were explicitly identi fied, rather than the similar to 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 N-a 1 independent conservation laws corresponding to nonlocal, mututally commu ting operators, which we call transfer-matrix currents. Further, for the mo del defined in the whole Hilbert space, we find there are two other indepen dent commuting operators (the squares of the eta -spin and spin operators) so that the total number. of local plus nonlocal commuting conservation law s for the one-dimensional Hubbard model is 2N(a) + 4. Finally, we introduce an alternative set of 2N(a) + 4 conservation laws which assume particularl y simple forms in terms of the pseudoparticle and Yang-particle operators. This set of mutually commuting operators lends itself more readily to calcu lations of physically relevant correlation functions at finite energy or fr equency than the previous set.