Abstract
In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × 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 N2a 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 La2CuO4 is shortly reviewed.
Highlights
The Hubbard model on a bipartite lattice is the simplest realistic toy model for description of the electronic correlation effects in general many-electron problems with short-range interaction on such a lattice
In this paper we review an application of the extended global SO(3) × SO(3) × U (1) symmetry of the Hubbard model on a square lattice
Such a rotated-electron related operational description is an application of the Hubbard model on a bipartite lattice extended global SO(3) × SO(3) × U (1) symmetry recently found in Reference [6]
Summary
The Hubbard model on a bipartite lattice is the simplest realistic toy model for description of the electronic correlation effects in general many-electron problems with short-range interaction on such a lattice. There is strong evidence that for approximately U/4t > 1, out of the infinite terms on the right-hand-side of Equation (6) only the first few Hamiltonian terms play an active role in the physics of the Hubbard model on the square lattice in the one- and two-electron subspace [10] This follows in part from in that subspace the rotated-electron configurations expressed in Reference [9] in terms of related c and s1 fermion operators referring to energy eigenstates. The unitarity and remaining properties of the electron-rotated-electron transformation considered in this paper assures that the corresponding c fermion, spinon, and η-spinon operator representation introduced in the following for U/4t > 0 applies as well to the Hubbard model on the square lattice
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