Emergence of integer quantum Hall effect from chaos

Abstract

We present an analytic microscopic theory showing that in a large class of spin-$\frac{1}{2}$ quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum ($h_e$) and the rotor's energy growth rate mimic the `filling fraction' and the `longitudinal conductivity' in conventional IQHE, respectively, and a hidden quantum number is found to mimic the `quantized Hall conductivity'. We show that for an infinite discrete set of critical values of $h_e$, the long-time energy growth rate is universal and of order of unity (`metallic' phase), but otherwise vanishes (`insulating' phase). Moreover, the rotor insulating phases are topological, each of which is characterized by a hidden quantum number. This number exhibits universal behavior for small $h_e$, i.e., it jumps by unity whenever $h_e$ decreases, passing through each critical value. This intriguing phenomenon is not triggered by the like of Landau band filling, well-known to be the mechanism for conventional IQHE, and far beyond the canonical Thouless-Kohmoto-Nightingale-Nijs paradigm for quantum Hall transitions. Instead, this dynamical phenomenon is of strong chaos origin; it does not occur when the dynamics is (partially) regular. More precisely, we find that, for the first time, a topological object, similar to the topological theta angle in quantum chromodynamics, emerges from strongly chaotic motion at microscopic scales, and its renormalization gives the hidden quantum number.Our analytic results are confirmed by numerical simulations.Our findings indicate that rich topological quantum phenomena can emerge from chaos and might point to a new direction of study in the interdisciplinary area straddling chaotic dynamics and condensed matter physics.

43 pages, 14 figures

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• Planck's quantum-driven integer quantum Hall effect in chaos
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Cited by in corpus (17)

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• Floquet topological phases in a spin-1/2 double kicked rotor
• Recipe for creating an arbitrary number of Floquet chiral edge states
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• Non-Hermitian Floquet Topological Matter -- A Review
• Controlling symmetry and localization with an artificial gauge field in a disordered quantum system
• Dynamical Localization of Coupled Relativistic Kicked Rotors
• Quantum simulation of disordered systems with cold atoms
• Experimental observation of time singularity in classical-to-quantum chaos transition
• Torsional Topological Invariants
• Quantum Hall criticality in Floquet topological insulators
• Entanglement spectrum and entropy in Floquet topological matter
• Floquet simulators for topological surface states in isolation
• Pseudoclassical dynamics of the kicked top
• Self-duality triggered dynamical transition
• Half-Quantized Hall Metal and Marginal Metal in Disordered Magnetic Topological Insulators
• Disordered Parity Anomalous Semimetal