  Within the framework of a mean-field approach the Mott-Hubbard phase
transition is considered in the Hubbard and Falicov-Kimball models for
half-filled occupation. It is shown that a static Z_2-field forms an insulator
state on the lattice with a double cell, its strength is determined by the
Hubbard interaction. An uniform configuration of the Z_2-field corresponds to a
gapless spin liquid state, the configuration, at which the lattice with a
double cell is formed, corresponds to a gapped fermion liquid, fermions move in
this field. Due to the presence of a static field in an insulator state, a
formation of a gapped electron liquid is similar to the gapless Majorana spin
liquid in Kitaev's model [1]. A gap in the spectrum is calculated depending on
the magnitude of the Hubbard interaction for the chain, square and cubic
lattices. The proposed approach allows us to describe the Mott-Hubbard phase
transition and the insulator state within the same formalism for an arbitrary
dimension for different models.
