The $SO(3)\times SO(3)\times U(1)$ Hubbard model on a square lattice in terms of $c$ and $\alpha \nu$ fermions and deconfined $\eta$-spinons and spinons

Abstract

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.

72 pages, 6 figures, in press in Annals of Physics (2012)

References in corpus (6)

• "Deconfined" quantum critical points
• A Mott insulator of fermionic atoms in an optical lattice
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Cited by in corpus (2)

• Charge dynamics in half-filled Hubbard chains with finite on-site interaction
• Spinon and eta-spinon correlation functions