We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Neel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.
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