An application of the extended global \(\mathrm{SO}(3)\times\mathrm{SO}(3)\times\mathrm U(1)\) symmetry of the Hubbard model on a square lattice: the spinon, \(\eta\)-spinon, and \(c\) fermion description (Q527586)

Summary: In this paper we review recent results on the preliminary applications of the new-found extended global \(\mathrm{SO}(3)\times\mathrm{SO}(3)\times\mathrm U(1)\) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral \(t\) and on-site repulsion \(U\) on a square lattice with \(N^2_a\gg 1\) sites consistent with its extended global symmetry. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global symmetry. Such objects emerge from a suitable electron-rotated-electron unitary transformation. An application to the spin spectrum of the parent compound \(\mathrm{La}_2\mathrm{CuO}_4\) is shortly reviewed.