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The experimental advances in cold atomic and molecular gases stimulate theinvestigation of lattice correlated systems beyond the conventional on-siteHubbard approximation, by possibly including multi-particle processes. We studyfermionic extended Hubbard models in a one dimensional lattice with differenttypes of particle couplings, including also three- and four-body interaction upto nearest neighboring sites. By using the Bosonization technique, weinvestigate the low-energy regime and determine the conditions for theappearance of ordered phases, for arbitrary particle filling. We find thatthree- and four-body couplings may significantly modify the phase diagram. Inparticular, diagonal three-body terms that directly couple the local particledensities have qualitatively different effects from off-diagonal three-bodycouplings originating from correlated hopping, and favor the appearance of aLuther-Emery phase even when two-body terms are repulsive. Furthermore, thefour-body coupling gives rise to a rich phase diagram and may lead to therealization of the Haldane insulator phase at half-filling.

Quantum phases of 1D Hubbard models with three- and four-body couplings