The angular-momentum aspect of Shift in FQHE

The angular momentum of the Hall particles acquiring Berry phases from quantization, is the very source of unifying the physics of IQHE and FQHE. The origin of Shift quantum number lies in the change of angular momentum of the Hall particles from higher to lower Landau level. The non-vanishing effect of Shift in 2D has been evaluated in the framework of Zp spin system and in view of these, Ising model and XY model are studied here.