Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopical characterization of non-Hermitian band structures   We proposed a framework towards the topological characterization of
non-Hermitian band structures. Different from previous $K$-theoretical
approaches, our approach is homotopical, which enables us to see more
topological invariants. Specifically, we considered the classification of
non-Hermitian systems with separable band structures. We found that the whole
classification set is decomposed into several sectors, based on the braiding of
energy levels. Each sector can be further classified based on the topology of
eigenstates (wave functions). Due to the interplay between energy level
braiding and eigenstates topology, we found some torsion invariants, which only
appear in the non-Hermitian world. We further proved that these new topological
invariants are unstable, in the sense that adding more bands will trivialize
these invariants.

27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex