2021/04/30 by Benoit Estienne, Blagoje Oblak, Jean-Marie Stéphan
Mathematics · Physics and Astronomy · #Condensed matter physics #Ergodic theory #Geometry #Magnetic field #Mathematical analysis #Mathematics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Torus #cond-mat.mes-hall #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.21468/scipostphys.11.1.016
published as SciPost Phys. 11, 016 (2021) · 24 pages + 17 pages, 18 figures. v2: added appendix E
arxiv created 2021/05/11 · openalex publication_date 2021/07/20 · arxiv updated 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The gapless modes on the edge of four-dimensional (4D) quantum Hall droplets are known to be anisotropic: they only propagate in one direction, foliating the 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive to the confining potential and generically yields chaotic flows. Here we study the quantum correlations and entanglement of such edge modes in 4D droplets confined by harmonic traps, whose boundary is a squashed three-sphere. Commensurable trapping frequencies lead to periodic trajectories of electronic guiding centers; the corresponding edge modes propagate independently along S1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> fibers, forming a bundle of 1D conformal field theories over a 2D base space. By contrast, incommensurable frequencies produce quasi-periodic, ergodic trajectories, each of which covers its invariant torus densely; the corresponding correlation function of edge modes has fractal features. This wealth of behaviors highlights the sharp differences between 4D Hall droplets and their 2D peers; it also exhibits the dependence of 4D edge modes on the choice of trap, suggesting the existence of observable bifurcations due to droplet deformations.