We derive the renormalization group equations describing all the short-range interactions in bilayer graphene allowed by symmetry and the long range Coulomb interaction. For certain range of parameters, we predict the first order phase transition to
the uniaxially deformed gapless state accompanied by the change of the topology of the electron spectrum.
We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions w
ith spin 1/2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.
