Abstract
It is shown that the Hubbard model with bond-charge interaction has SO(4) symmetry at half-filling. The η pairing symmetry leads to some new collective modes, which may be detected experimentally. The Goldstone mode exists in the η pairing ground state. The system is also found to be a supersolid in this state. The existence of ferromagnetic long-range order at half-filling is proven in the ground state as the parameters satisfy U ≥ 2| t| Z, which is independent of geometries of lattices and space dimensions.
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