Magnetic Orders of Correlated Topological Insulators at Finite Temperature

In this paper, we study the magnetic orders of two dimensional correlated topological insulators including the correlated Chern insulator and the correlated Z2 topological insulator at finite temperature. For the 2D correlated Chern insulator, we found that thermal-fluctuation-induced magnetic order appears in the intermediate interaction region of the correlated Chern insulator. On the contrary, for the correlated Z2 topological insulator there doesn't exist the thermal-fluctuation-induced magnetic order. In the end, we give an explanation on the difference.