Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on "Experimental Measurement of Quantum Metric Tensor and Related
  Topological Phase Transition with a Superconducting Qubit"   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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The categories of this paper are: supr-con
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex