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arXiv · 1908.06462

Note on "Experimental Measurement of Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit"

Yan-Qing Zhu·Dan-Wei Zhang·Xinsheng Tan·Hai-Feng Yu·Hui Yan·Yang Yu·Shi-Liang Zhu
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Abstract

In the paper [X. Tan et al., Phys. Rev. Lett. 122, 210401 (2019)], we have studied the Euler characteristic number $\chi$ for a two-band model; However, the calculated $\chi$ 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.

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Yan-Qing Zhu, Dan-Wei Zhang, Xinsheng Tan, Hai-Feng Yu, Hui Yan, Yang Yu, Shi-Liang Zhu. 2019-08-18. Note on "Experimental Measurement of Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit". https://arxiv.org/abs/1908.06462

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