We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet
dxy-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet
py-wave-like pairing correlation is most dominant.
We study an asymmetric ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladder consisting of two different spin-
21 antiferromagnetic (AFM; ${J}_{2}, \ensuremath{\gamma}{J}_{2}>0$) Heisenberg legs coupled by zigzag-shaped ferromagnetic (FM;
J1<0) interleg interaction. On the basis of density-matrix renormalization group based calculations, the ground-state phase diagram is obtained as functions of $\ensuremath{\gamma}$ and
J2/∣J1∣. It contains four kinds of frustration-induced ordered phases except a trivial FM phase. Two of the ordered phases are valence bond solid (VBS) with spin-singlet dimerization, which is a rather conventional order by disorder. Still, it is interesting to note that the VBS states possesses an Affleck-Kennedy-Lieb-Tasaki--type topological hidden order. The remaining two phases are ferrimagnetic orders, each of which is distinguished by commensurate or incommensurate spin-spin correlation. It is striking that the ferrimagnetic orders are not associated with geometrical symmetry breaking; instead, the global spin-rotation symmetry is broken. In other words, the system lowers its energy via the FM interleg interaction by polarizing both of the AFM Heisenberg legs. This is a rare type of order by disorder. Besides, the incommensurate ferrimagnetic state appears as a consequence of the competition between a polarization and a critical Tomonaga-Luttinger--liquid behavior in the AFM Heisenberg legs.
We study magnetic properties of a periodically driven Mott insulator with strong spin-orbit coupling and show some properties characteristic of linearly polarized light. We consider a
t2g-orbital Hubbard model driven by circularly or linearly polarized light with strong spin-orbit coupling and derive its effective Hamiltonian in the strong-interaction limit for a high-frequency case. We show that linearly polarized light can change not only the magnitudes and signs of the exchange interactions, but also their bond anisotropy even without the bond-anisotropic hopping integrals. Because of this property, the honeycomb-network spin system could be transformed into weakly coupled zigzag or step spin chains for the light field polarized along the
b or
a axis, respectively. Then, analyzing how the light fields affect several magnetic states in a mean-field approximation, we show that linearly polarized light can change the relative stability of the competing magnetic states, whereas such a change is absent for circularly polarized light. We also analyze the effects of both the bond anisotropy of nearest-neighbor hopping integrals and a third-neighbor hopping integral on the magnetic states and show that the results obtained in a simple model, in which the bond-averaged nearest-neighbor hopping integrals are considered, remain qualitatively unchanged except for the stability of zigzag states in the nondriven case and the degeneracy lifting of the zigzag or stripy states.