FLUX-QUANTIZATION ON A LATTICE

We calculated the ground state energy and the magnetization of spinless fermions on the two-dimensional lattice in the Hartree-Fock approximation. The diamagnetism of the lattice has an unusual form and is equivalent to the diamagnetism of a superconducting ring. We find that the lattice with spinless free electrons at zero temperature can trap an even number of the magnetic flux quanta. Each trapping of the flux quanta corresponds to the transition to a new ground state with the quantum number of the total flux. For each state the flux of the external magnetic field is absolutely screened (Meissner effect). We show that at high temperature it is possible the existence of the states with the fractional flux quanta. By comparison with previous results, we find the criterion for the existence of the "commensurate flux phase" states.