The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.The one band Hubbard model on a bi-partite lattice possess a global SO(4) symmetry group which is a direct product of the spin SU(2) and the pseudospin SU(2) symmetry group. Recently, the group theorectical consequence of this symmetry property has been investigated systematically. It is shown that this symmetry property can be used to reduce the complexity of diagonalizing the Hubbard Hamiltonian, and classify all the eigenstates according to the representation of the SO(4) group. It also leads to an exact one-to-one corespondence of the eigenstates at half-filling to that away from half-filling. Most importantly however, it is shown that this symmetry property leads to a direct experimental prediction for the high Tc superconductivity. If the high Tc superconductivity is correctly described by the Hubbard model, then the SO(4) symmetry dictates the existence of a collective mode that only appears below the superconducting transition temperature. Such a mode can be detected in an electron energy loss experiment as a sharp resonance feature. The location of the peak measure the parameters in the Hubbard model, the intensity is proportional to the superconducting order parameter and the width measures the departure of the Hubbard model from reality.

International Journal of Modern Physics BJan 1, 199128 citations

Ward-Takahashi relations for SO(4) symmetry in the Hubbard model

Atsushi Masumizu, Kiyoshi Sogo

Ward-Takahashi relations for spin symmetry $\mathrm{SU}{(2)}_{\mathrm{S}}$ and pseudospin symmetry $\mathrm{SU}{(2)}_{\mathrm{C}}$ are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.Ward-Takahashi relations for spin symmetry $\mathrm{SU}{(2)}_{\mathrm{S}}$ and pseudospin symmetry $\mathrm{SU}{(2)}_{\mathrm{C}}$ are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.

Physical Review BSep 12, 20057 citations

SO 4 SYMMETRY IN A HUBBARD MODEL

Chen Ning Yang, S.-C. Zhang

Series on advances in statistical mechanicsJul 1, 19910 citations

SO 4 SYMMETRY IN A HUBBARD MODEL

Chen Ning Yang, S.-C. Zhang

WORLD SCIENTIFIC eBooksApr 30, 20133 citations

Ward-Takahashi relations for spin symmetry

\mathrm{SU}{(2)}_{\mathrm{S}}

and pseudospin symmetry

\mathrm{SU}{(2)}_{\mathrm{C}}

are derived for the simple Hubbard model in arbitrary dimensions. For this purpose we generally discuss local SO(4) symmetry in terms of Clifford algebra, and employ a gauge transformed form of the original Hubbard Hamiltonian, which makes the Ward-Takahashi relations much simpler. Derived Ward-Takahashi relations are rewritten as the relations between self-energy and vertex part to discuss spontaneously broken symmetry and Fermi liquid property of the system for zero temperature magnetism.