1211.5391 (J. M. P. Carmelo)

Elementary objects of the 1D Hubbard model from its symmetry and exact
solution I    [PDF]

J. M. P. Carmelo

In this first paper of a series of two, we uniquely define the exotic elementary objects that emerge from the interplay of the 1D Hubbard model recently found global $[SU(2)\otimes SU(2)\otimes U(1)]/Z_2^2$ symmetry with the exact Bethe-ansatz (BA) solution. Their occupancy configurations generate the exact energy eigenstates of the model. The results refer to the limit of a very large system in which the thermodynamic BA equations apply. The BA solution choses one of the infinite electron - rotated-electron unitary transformations such that rotated-electron single and double occupancy are a good quantum number for any finite interaction value. This allows a precise operational definition of three exotic elementary objects whose occupancy configurations generate all exact energy eigenstates: spin-less and $\eta$-spin-less $c$ fermions, spin-1/2 spinons, and $\eta$-spin-1/2 $\eta$-spinons. In the second paper the scattering theory associated with the present elementary objects is constructed. That study reveals that there is no contradiction whatsoever between the present elementary-object description and those in terms of traditional spinons and holons.

View original: http://arxiv.org/abs/1211.5391