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

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, $\sigma^{*}=0.3253(12)$.