M. V. Ulybyshev, M. A. Zubkov
We consider the low energy effective field model of graphene monolayer. Coulomb interaction between the quasiparticles is taken into account. This model is simulated numerically using the lattice discretization with staggered fermions. Momentum space topology of this lattice model is investigated. The positions of momentum space monopoles and vortices are calculated and visualized for the first time. We investigate the model at the two points on the phase diagram that correspond to the values of the effective coupling constant $\beta = 0.2, 0.05$. At the first point that corresponds to the semi - metal phase there exist 8 monopoles in momentum space. One of them corresponds to the massless fermionic excitation while the other 7 monopoles correspond to the massive unphysical doublers that disappear in the continuum limit. At $\beta = 0.05$ that is deep in the insulator phase the fermionic Green function almost does not depend on energy. This means that different time slices correlate with each other very weakly and the system is described by the effective two - dimensional model rather than by the 2+1 model. In this case the momentum space monopoles are not relevant. Instead we observe 4 vortices in momentum space. We suppose that one of them is related to the generation of the screening mass while the others correspond to the unphysical doublers.
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http://arxiv.org/abs/1205.0888
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