2019/08/18 by Zhu, Yan-Qing, Zhang, Dan-Wei, Tan, Xinsheng +4
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1908.06462
In the paper [X. Tan et al., Phys. Rev. Lett. 122, 210401 (2019)], we have studied the Euler characteristic number χ for a two-band model; However, the calculated χ there is not an integer when the parameter |h|>1 and then may not be considered as a suitable topological number for the system. In this note, we find that the Bloch vectors of the ground state for |h|>1 do not cover the whole Bloch sphere and thus the Euler characteristic number should be effectively associated with the manifold of a disk, rather than a sphere. After taking into account the boundary contribution, we derive the correct Euler characteristic number. Unfortunately, the Euler characteristic number does not change when crossing the critical points |h|=1 and thus can not be used to characterize the topological phase transition of the present model.