Order-from-disorder effects and Zeeman field tuned quantum phase transitions in a bosonic quantum anomalous Hall system

We study possible many body phenomena in the recent experimentally realized weakly interacting quantum anomalous Hall system of spinor bosons by Wu, et.al, Science 354, 83-88 (2016). At a zero Zeeman field h = 0, by incorporating order from disorder effects, we determine the quantum ground state to be a N = 2 XY-antiferromagnetic superfluid state and also evaluate its excitation spectra. At a finite small h, the competition between the Zeeman energy and the effective potential generated by the order-from-disorder leads to a canted antiferromagnetic superfluid state, then drives a second order transition to a spin-polarized superfluid state along the z direction. The transition is in the same universality class as the zero density superfluid to Mott transition. Scaling behaviours of various physical quantities are derived. The ongoing experimental efforts to detect these novel phenomena are discussed.