Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry indicators vs. bulk winding numbers of topologically
  non-trivial bands   The symmetry-indicators provide valuable information about the topological
properties of band structures in real materials. For inversion-symmetric,
non-magnetic materials, the pattern of parity eigenvalues of various
Kramers-degenerate bands at the time-reversal-invariant momentum points are
generally analyzed with the combination of strong $Z_4$, and weak $Z_2$
indices. Can the symmetry indicators identify the tunneling configurations of
SU(2) Berry connections or the three-dimensional, winding numbers of
topologically non-trivial bands? In this work, we perform detailed analytical
and numerical calculations on various effective tight-binding models to answer
this question. If the parity eigenvalues are regarded as fictitious Ising
spins, located at the vertices of Miller hypercube, the strong $Z_4$ index
describes the net ferro-magnetic moment, which is shown to be inadequate for
identifying non-trivial bands, supporting even integer winding numbers. We
demonstrate that an anti-ferromagnetic index, measuring the staggered
magnetization can distinguish between bands possessing zero, odd, and even
integer winding numbers. The coarse-grained analysis of symmetry-indicators is
substantiated by computing the change in rotational-symmetry-protected,
quantized Berry flux and Wilson loops along various high-symmetry axes. By
simultaneously computing ferromagnetic and anti-ferromagnetic indices, we
categorize various bands of bismuth, antimony, rhombohedral phosphorus, and
Bi$_2$Se$_3$.

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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex