Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupling, merging, and splitting Dirac points by electron-electron
  interaction   The manipulation and movement of Dirac points in the Brillouin zone by the
electron-electron interaction is considered within leading order perturbation
theory. At the merging point, an infinitesimal interaction is shown to cause
opening of the gap or splitting of the Dirac points, depending on the inter- or
intrasublattice nature of the merging and the sign of the interaction. The
topology of the spectrum can therefore be efficiently changed by simply tuning
the interaction between particles, as opposed to the usual careful band
structure engineering. This is illustrated around the merging transition of
one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like
Hamiltonian that describes the quadratic band-crossing in three dimensions is
also proposed, and its stability under interactions is addressed.

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph