We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with
power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. Notably, the observed flux quanta are determined by the difference between the system size NL and electron number N_e as h=(N_L-N_e)e.
We show that a hole and a triplet spin form a bound state in a nearly half-filled band of the one- and two-dimensional $t_1$-$t_2$-$J_1$-$J_2$ models. Numerical calculation indicates that the bound state is a spatially small object and moves as a com
posite particle with spin 1 and charge $+e$ in the spin-gapped background. Two bound states repulsively interact with each other in a short distance and move independently as long as they keep their distance. If a finite density of bound states behave as bosons, the system undergoes the Bose-Einstein condensation which means a superconductivity with charge $+e$.
We investigate the electronic states of a one-dimensional two-orbital Hubbard model with band splitting by the exact diagonalization method. The Luttinger liquid parameter $K_{rho}$ is calculated to obtain superconducting (SC) phase diagram as a func
tion of on-site interactions: the intra- and inter-orbital Coulomb $U$ and $U$, the Hund coupling $J$, and the pair transfer $J$. In this model, electron and hole Fermi pockets are produced when the Fermi level crosses both the upper and lower orbital bands. We find that the system shows two types of SC phases, the SC Roman{u-large} for $U>U$ and the SC Roman{u-large} for $U<U$, in the wide parameter region including both weak and strong correlation regimes. Pairing correlation functions indicate that the most dominant pairing for the SC Roman{u-large} (SC Roman{u-large}) is the intersite (on-site) intraorbital spin-singlet with (without) sign reversal of the order parameters between two Fermi pockets. The result of the SC Roman{u-large} is consistent with the sign-reversing s-wave pairing that has recently been proposed for iron oxypnictide superconductors.
