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We give a brief summary of the current status of the electron many-body problem in graphene. We claim that graphene has intrinsic dielectric properties which should dress the interactions among the quasiparticles, and may explain why the observation of electron-electron renormalization effects has been so elusive in the recent experiments. We argue that the strength of Coulomb interactions in graphene may be characterized by an effective fine structure constant given by $alpha^{star}(mathbf{k},omega)equiv2.2/epsilon(mathbf{k},omega)$, where $epsilon(mathbf{k},omega)$ is the dynamical dielectric function. At long wavelengths, $alpha^{star}(mathbf{k},omega)$ appears to have its smallest value in the static regime, where $alpha^{star}(mathbf{k}to0,0)approx1/7$ according to recent inelastic x-ray measurements, and the largest value in the optical limit, where $alpha^{star}(0,omega)approx2.6$. We conclude that the strength of Coulomb interactions in graphene is not universal, but depends highly on the scale of the phenomenon of interest. We propose a prescription in order to reconcile different experiments.
Do electrons become ferromagnetic just because of their repulisve Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetim of delocalized electrons without lattice and band structure, the most bas
We study the zero-temperature many-body properties of twisted bilayer graphene with a twist angle equal to the so-called `first magic angle. The system low-energy single-electron spectrum consists of four (eight, if spin label is accounted) weakly-di
Motivated by the intriguing physics of quasi-2d fermionic systems, such as high-temperature superconducting oxides, layered transition metal chalcogenides or surface or interface systems, the development of many-body computational methods geared at i
We generalize Pages result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long range interactions. This extension leads to two principal conclusions: first, for incr
Impressive advances in the field of molecular spintronics allow one to study electron transport through individual magnetic molecules embedded between metallic leads in the purely quantum regime of single electron tunneling. Besides fundamental inter