Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comment on 'Winding around non-Hermitian singularities' by Zhong et al.,
  Nat. Commun. 9, 4808 (2018)   In a recent paper entitled "Winding around non-Hermitian singularities" by
Zhong et al., published in Nat. Commun. 9, 4808 (2018), a formalism is proposed
for calculating the permutations of eigenstates that arise upon encircling
(multiple) exceptional points (EPs) in the complex parameter plane of an
analytic non-Hermitian Hamiltonian. The authors suggest that upon encircling
EPs one should track the eigenvalue branch cuts that are traversed, and
multiply the associated permutation matrices accordingly. In this comment we
point out a serious shortcoming of this approach, illustrated by an explicit
example that yields the wrong result for a specific loop. A more general method
that has been published earlier by us and that does not suffer from this
problem, is based on using fundamental loops. We briefly explain the method and
list its various advantages. In addition, we argue that this method can be
verified in a three wave-guide system, which then also unambiguously
establishes the noncommutativity associated with encircling multiple EPs.

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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: econ