Finite-Size Scaling Analysis of the Planck's Quantum-Driven Integer Quantum Hall Transition in Spin-$1/2$ Kicked Rotor Model

TL;DR

This paper applies finite-size scaling analysis to a spin-1/2 quantum kicked rotor model to study transitions analogous to the integer quantum Hall effect, estimating critical exponents and universal diffusion rates.

Contribution

It introduces a finite-size scaling method to analyze IQH-like transitions in the spin-1/2 QKR and provides precise estimates of critical parameters.

Findings

Critical exponent ν=2.62(9) consistent with IQH universality class

Universal diffusion rate at critical state σ*=0.3253(12)

Finite-size scaling effectively characterizes quantum Hall transitions in QKR

Abstract

The quantum kicked rotor (QKR) model is a prototypical system in the research of quantum chaos. In a spin-$1/2$ QKR, tuning the effective Planck parameter realizes a series of transitions between dynamical localization phases, which closely resembles the integer quantum Hall (IQH) effect and the plateau transitions. In this work, we devise and apply the finite-size scaling analysis to the transitions in the spin-$1/2$ QKR model. We obtain an estimate of the critical exponent at the transition point, $\nu=2.62(9)$, which is consistent with the IQH plateau transition universality class. We also give a precise estimate of the universal diffusion rate at the metallic critical state, $\sigma^{*}=0.3253(12)$.