The Angular momentum aspect of shift in FQHE

TL;DR

This paper explores how the angular momentum of particles in the fractional quantum Hall effect (FQHE), influenced by Berry phases, explains the shift quantum number and unifies the understanding of IQHE and FQHE.

Contribution

It introduces a framework using $Z_p$ spin systems to analyze the shift quantum number and studies related models like Ising and XY to understand angular momentum effects.

Findings

Shift quantum number arises from angular momentum change between Landau levels.

Berry phases influence the angular momentum of Hall particles.

The $Z_p$ spin system framework links angular momentum to quantum Hall phenomena.

Abstract

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 {\it Shift} quantum number lies in the change of angular momentum of the Hall particles from higher to lower Landau level. Here the non-vanishing effect of {\it Shift} in 2D has been evaluated in the framework of $Z_p$ spin system and in view of these, Ising model and XY model are studied.