Exotic spin phases in two-dimensional spin-orbit coupled models: Importance of quantum effects

We investigate the phase diagrams of the effective spin models derived from Fermi-Hubbard and Bose-Hubbard models with Rashba spin-orbit coupling, using string bond states, one of the quantum tensor network states methods. We focus on the role of quantum fluctuation effect in stabilizing the exotic spin phases in these models. For boson systems, and when the ratio between interparticle and intraparticle interaction lambda > 1, the out-of-plane ferromagnetic (FM) and antiferromagnetic (AFM) phases obtained from quantum simulations are the same as those obtained from the classic model. However, the quantum order-by-disorder effect reduces the classical in-plane XY-FM and XY-vortex phases to the quantum X/Y-FM and X/Y-stripe phase when lambda < 1. The spiral phase and skyrmion phase can be realized in the presence of quantum fluctuation. For the Fermi-Hubbard model, the quantum fluctuation energies are always important in the whole parameter regime. A general picture to understand the phase diagrams from a symmetry point of view is also presented.