Conservation laws in the one-dimensional Hubbard model

Abstract

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 (N{sub a}), only N{sub a}+1 conservation laws, corresponding to N{sub a}+1 operators that commute with themselves and the Hamiltonian, were explicitly identified, rather than the {approx}2N{sub 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{sub a}+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 {eta}-spin and spin operators) so that the total number of local plus nonlocal commuting conservation laws for the one-dimensional Hubbard model is 2N{sub a}+4. Finally, we introduce an alternative set of 2N{sub a}+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 readilymore » to calculations of physically relevant correlation functions at finite energy or frequency than the previous set.« less