Eur. Phys. J. B (2013) 86: 379
https://doi.org/10.1140/epjb/e2013-31040-6

Regular Article

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

State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, P.R. China

^a e-mail: stslsd@mail.sysu.edu.cn
^b e-mail: yaodaox@mail.sysu.edu.cn

Received: 14 November 2012
Received in final form: 17 July 2013
Published online: 11 September 2013

Abstract

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.