Transitions from the Quantum Hall State to the Anderson Insulator: Fa te of Delocalized States

TL;DR

This paper investigates the transition between quantum Hall states and Anderson insulators in a 2D model, analyzing delocalized states and Hall conductance changes using numerical and topological methods.

Contribution

It provides a numerical study of the transition regime in a 2D tight-binding model with magnetic field and disorder, linking weak field behavior to continuum models.

Findings

Delocalized states' trajectories are mapped during the transition.

Hall conductance changes are characterized topologically.

The weak magnetic field regime closely relates to continuum models.

Abstract

Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is explored numerically. The regime is closely related to the continuum model. The change of the Hall conductance and the trajectoy of the delocalized states are investigated by the topological arguments and the Thouless number study.