Metallic phase of the quantum Hall effect in four-dimensional space

TL;DR

This paper explores the phase diagram of the 4D quantum Hall effect, revealing metallic and insulating phases depending on disorder, and provides numerical methods for potential experimental realization.

Contribution

It introduces a numerical approach to study the 4D quantum Hall effect and identifies a unique metallic phase not present in lower dimensions.

Findings

Existence of metallic and insulating phases in 4D quantum Hall effect

Critical exponent of the transition is approximately 1.2

Mapping of 4D Hamiltonian to a 1D dynamical system

Abstract

We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent $\nu\approx 1.2$ of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value $\nu=1$ of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route towards the experimental realization of the 4D quantum Hall effect.