We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping ${t}^{\ensuremath{'}}$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two Van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two Van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from interband contributions to the spin susceptibility. These interband contributions only arise if there is one holelike and one electronlike Fermi surface, which is the case for fillings in between the two Van Hove fillings. We discuss implications for experimental systems and propose a test on how to identify these types of ferromagnetic fluctuations in experiments.
We present a theory to realize fractionally magnetized quantum ferromagnet in a
spin−S≧2bilinear-biquadratic spin systems. The origin of the fractionally magnetized state is spin-liquefaction of ferromagnetism which means partly emergent antiferromagnetism. The realization of the spin-liquefaction of ferromagnetism is guaranteed due to a rigorous eigenstate correspondence between the
Spin−Smodel and
spin−21model, i. e., “eigensystem embedding”. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices. As a typical case, we discuss the two-dimensional models on a square lattice with a numerical exact-diagonalization.
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system with the hard constraints replaced by soft constraints. I illustrate the method in the case of the ferromagnetic Ising model and in the case the three dimensional spin-glass model. I show in both the ferromagnetic Ising and the spin-glass model that the phases of the soft problem have the same properties with the phases of the original model and that the softened model belongs to the same universality class as the original one. I show that correlation times are much shorter in the larger soft constrained system and that it is computationally advantageous to study it instead of the original system. This method is quite general and can be applied to other systems.