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Highlights • We extend the 1D t – U – J x y model up to NNN easy-plane anisotropy. • We derive quantum phase diagram at weak coupling and at half filling. • The effects of the frustration on the phase diagram is highlighted. • The mechanism for the realization of two spin-gapped phases is clarified. Abstract At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy J 1 x y and J 2 x y. At half filling, we obtain three different phases in the J 1 x y – J 2 x y plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange J 2 x y accounts for the spin-gapped phases. [ABSTRACT FROM AUTHOR]

The experimental advances in cold fermion gases motivates the investigation of a one-dimensional (1D) correlated electronic system by incorporating a four-body coupling. Using the low-energy field theory scheme and focusing on the weak-coupling regime, we extend the 1D Penson–Kolb–Hubbard (PKH) model at half filling. It is found that the additional four-body interaction may significantly modify the quantum phase diagram, favoring the presence of the superconducting phase even in the case of two-body repulsions. [ABSTRACT FROM AUTHOR]

Applying the bosonization and renormalization group techniques, we study a generalized Hubbard chain incorporating extra off-diagonal hopping processes in the weak regime, and determine rich ground-state phase diagrams. At half filling, in addition to the insulating phases (HI, MI and DI), there exist the superconducting phases (LE and LL). The off-diagonal hopping accounts for the occurrence of insulator-superconductor transition. Away from half filling, the transition from the LL to LE phase takes place, and the insulating phases disappear. The result provides an insignificant insight into unconventional scenarios for Cooper pairing and insulator-superconductor transition. [ABSTRACT FROM AUTHOR]

We construct a one-dimensional (1D) theoretical model to clarify the occurrence of superconductivity. The weak-coupling (WC) theory allows a determination of the phase diagram. The constrained hopping induces additional two-body and three-body interactions. At half-filling, the three-body interaction is responsible for the triplet superconducting (TS) correlation. Away from half-filling, the two-body interaction works, favoring the singlet superconducting (SS) correlation. The results are expected to provide an insignificant insight into the superconductivity mechanism. [ABSTRACT FROM AUTHOR]

At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U , V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V , the attractive P may give rise to the superconducting phases for 2 V ≤ min { 2 | P | ; 4 | P | − U }. • We study the 1D extended Hubbard model with three-body interaction. • The attractive three-electron coupling leads to superconducting phases. • The study supplements understanding of quantum properties of 1D correlated systems. [ABSTRACT FROM AUTHOR]