Quantum Hall effect in a one-dimensional dynamical system

TL;DR

This paper demonstrates a method to realize the quantum Hall effect in a one-dimensional system by using a time-dependent Hamiltonian with incommensurate frequencies, enabling efficient computation and potential experimental simulation.

Contribution

It introduces a 1D model with a phase transition in the quantum Hall class, simplifying the study and experimental realization of quantum Hall phenomena.

Findings

Reduction of 2D quantum Hall system to 1D via incommensurate driving

Efficient computational modeling of quantum Hall effect in 1D

Potential for cold atom experiments to simulate 2D quantum Hall physics

Abstract

We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.