Abstract
A low-energy physics of a one-dimensional interacting electron system at half filling is constructed. Beyond the usual two-body approximation, the two different types of three-body couplings are highlighted. The rich ground-state phase diagrams are obtained at weak coupling. In the case of two-body repulsions, the off-diagonal three-body coupling favors the bond-located density-wave insulating phases, while the diagonal three-body attraction favors the superconducting phases.
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