1003.4499 (J. M. P. Carmelo)

The $SO(3)\times SO(3)\times U(1)$ Hubbard model on a square lattice in
terms of $c$ and $αν$ fermions and deconfined $η$-spinons and
spinons    [PDF]

J. M. P. Carmelo

In this paper a description of the energy eingenstates of the Hubbard model
on the square lattice with nearest-neighbor transfer integral $t$, on-site
repulsion $U$, and $N_a^2\gg 1$ sites in terms of occupancy configurations of
charge $c$ fermions, spin-1/2 spinons, and $\eta$-spin-1/2 $\eta$-spinons is
introduced. Such objects emerge from a suitable electron - rotated-electron
unitary transformation. In chromodynamics the quarks have color but all
quark-composite physical particles are color-neutral. Within our description
the $\eta$-spinon (and spinons) that are not invariant under the electron -
rotated-electron unitary transformation have $\eta$ spin 1/2 (and spin 1/2) but
are part of $\eta$-spin-neutral (and spin-neutral) $2\nu$-$\eta$-spinon (and
$2\nu$-spinon) composite $\eta\nu$ fermions (and $s\nu$ fermions). Here
$\nu=1,2,...$ is the number of $\eta$-spinon (and spinon) pairs. In turn, a
well-defined number of independent spinons and independent $\eta$-spinons are
invariant under the electron - rotated-electron unitary transformation. Simple
occupancy configurations of (i) the $c$ fermions, (ii) independent spinons and
$2\nu$-spinon composite $s\nu$ fermions, and (iii) independent $\eta$-spinons
and $2\nu$-$\eta$-spinon composite $\eta\nu$ fermions generate an useful
complete set of states. The configurations (i), (ii), and (iii) correspond to
the state representations of the U(1), spin SU(2), and $\eta$-spin SU(2)
symmetries, respectively, associated with the model $SO(3)\times SO(3)\times
U(1) =[SU(2)\times SU(2)\times U(1)]/Z_2^2$ global symmetry.

View original: http://arxiv.org/abs/1003.4499