Magnetization plateaus of frustrated antiferromagnet and analogy with FQHE

An exact diagonalization technique was used to investigate the eigenstates of the two-dimensional frustrated spin 12 Heisenberg antiferromagnet on the 4 × 4 square lattice in the subspaces with the different full magnetization M. The energies of these states, spin-spin correlation functions and the magnetization as a function of the external magnetic field H were obtained. The set of plateaus on the M = M(H) plot are discovered. This confirms more deep analogy between the frustrated antiferromagnet and the fractional quantum Hall effect than the ordinary one supposed. The sizes of plateaus and their locations depend on the type of the lattice and on the degree of frustration.