Magnetization plateaus in one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization

The one dimensional S = 1/2 Heisenberg model with dimerization (1 - j) and quadrumerization (delta) in the magnetic field is studied by means of the numerical exact diagonalization of finite size systems and the conformal field theory. It is found that the magnetization plateau at half of the saturation value exists for delta not equal 0. For delta = 0, this model is described by the conformal field theory with central charge c = 1 at this value of magnetization. The critical exponent upsilon which characterizes the delta-dependence of the width of the plateau is calculated using the level spectroscopy method. The j-dependence of the critical exponent upsilon is found to be non-monotonic and discontinuous at j = 0. The effective theory of the magnetization plateau is also presented for various limiting cases.