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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.