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

• URL: http://arxiv.org/abs/2112.02748v1
• Date: Mon, 6 Dec 2021 02:51:31 GMT
• Title: Finite-Size Scaling Analysis of the Planck's Quantum-Driven Integer Quantum Hall Transition in Spin-$1/2$ Kicked Rotor Model
• Authors: Jia-Long Zhang, Long Zhang, Fu-Chun Zhang
• Abstract summary: The quantum kicked rotor (QKR) model is a prototypical system in the research of quantum chaos. In this work, we devise and apply the finite-size scaling analysis to the transitions in the spin-$1/2$ QKR model.
• Score: 3.819941837571746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, $\sigma^{*}=0.3253(12)$.

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