Transitions Between Hall Plateaus and the Dimerization Transition of a Hubbard Chain

TL;DR

This paper demonstrates that quantum Hall plateau transitions are equivalent to the dimerization transition in a one-dimensional Hubbard model, analyzing critical and off-critical properties through renormalization group and Monte Carlo methods.

Contribution

It establishes a novel equivalence between quantum Hall plateau transitions and a specific Hubbard model transition, providing new insights into their critical behavior.

Findings

Quantum Hall plateau transitions match the dimerization transition in the Hubbard model.

Critical properties are characterized using renormalization group analysis.

Monte Carlo simulations support the theoretical findings.

Abstract

We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, $U(2n)$ Hubbard model at $n=0$. We address the properties of the latter by a combination of perturbative renormalization group and Monte Carlo simulations. Results on both critical and off-critical properties are presented.