Mott-Hubbard phase transition in 2D electron liquid

We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+\pi$ are coupled via the effective $\lambda$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~$U_c$. $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.