Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Winding vector: how to annihilate two Dirac points with the same charge   The merging or emergence of a pair of Dirac points may be classified
according to whether the winding numbers which characterize them are opposite
($+-$ scenario) or identical ($++$ scenario). From the touching point between
two parabolic bands (one of them can be flat), two Dirac points with the {\it
same} winding number emerge under appropriate distortion (interaction, etc),
following the $++$ scenario. Under further distortion, these Dirac points merge
following the $+-$ scenario, that is corresponding to {\it opposite} winding
numbers. This apparent contradiction is solved by the fact that the winding
number is actually defined around a unit vector on the Bloch sphere and that
this vector rotates during the motion of the Dirac points. This is shown here
within the simplest two-band lattice model (Mielke) exhibiting a flat band. We
argue on several examples that the evolution between the two scenarios is
general.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat