Edge states and topological orders in the spin liquid phases of star lattice

The integer quantum Hall effect (IQHE) on star lattice is studied through edge states in the context of spin liquid. We apply the bulk-edge correspondence to the star lattice and analyze the edge states and their topological orders for different spin liquid phases. The band structures and Chern number depend on the local spontaneous magnetic flux and hopping parameters due to the breaking of the time reversal and space inversion symmetries. We give the characteristics of bulk and edge energy structures and their corresponding Chern numbers in the uniform, nematic and chiral spin liquids. In particular, we obtain analytically the phase diagram of the topological orders for the chiral spin liquid states SL[φ,φ,−2φ], where φ is the magnetic flux in two triangles and a dodecagon in one unit cell. Moreover, because of the direct connection between Chern number and the conductance of IQHE, we can further distinguish the different spin liquid phases through a Hall measurement.