Abstract
We discuss the exact bond-ordered ground states of the one-dimensional half-filled generalized Hubbard model including three- and four-body terms, by decomposing the Hamiltonian into positive semidefinite parts. The obtained exact ground states are interpreted as N\'eel ordered states on the bond-located electrons. We determine parameter regions of the exact ground states. We also calculate elementary excitation energies as variational approach based on the matrix-product formalism.
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