  The Kondo insulator state (KIS) is among the least understood phase state in
condensed matter physics. KIS is the state of the electron liquid in the Kondo
lattice at half filling, is studied within the mean field approach. We
demonstrate, that $Z_2$-field, which is formed by electrons and local moments,
leads to the state of the Kondo insulator in a lattice with a double cell. In
the ground state, electrons and local moments form singlets; in this case, no
spin or charge density waves are realized in a lattice with a double cell. We
have shown that a Majorana-type gap spectrum of the quasi-particle excitations
is realized in $Z_2$-field.8 pages The gap in the spectrum decreases with
increasing external magnetic field; it closes at a critical value at the
insulator-metal phase transition point. Thus, the introduction of the $Z_2$
-field allows you to answer the key question what is the ground state of KIS.
