# Ergodic Edge Modes in the 4D Quantum Hall Effect

### Submission summary

 As Contributors: Benoit Estienne · Blagoje Oblak Arxiv Link: https://arxiv.org/abs/2104.01860v2 (pdf) Date accepted: 2021-07-16 Date submitted: 2021-05-12 06:39 Submitted by: Oblak, Blagoje Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

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 $S^1$ 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.

Published as SciPost Phys. 11, 016 (2021)

### Submission & Refereeing History

Submission 2104.01860v2 on 12 May 2021

## Reports on this Submission

### Anonymous Report 2 on 2021-7-12 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2104.01860v2, delivered 2021-07-12, doi: 10.21468/SciPost.Report.3223

### Strengths

This is an excellent article, addressing a very relevant problem, and carrying out a comprehensive analysis. I have gone through the paper carefully, and I have no specific critical comments. I recommend publication.

Regarding the specific criteria, I would say that this does provide a novel and synergetic link between different research areas.

### Report

As explained in the earlier statements, this does provide a novel and synergetic link between different research areas, thus meeting the journal criteria.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Anonymous Report 1 on 2021-7-10 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2104.01860v2, delivered 2021-07-10, doi: 10.21468/SciPost.Report.3221

### Report

This manuscript deals with various aspects of integer 4D QHE, in particular the edge degrees of freedom and their contribution to the entanglement entropy.
This is a detailed, well written paper of interest to the wider condensed-matter community.
I do not have any suggestions for changes and I strongly recommend publication.

• validity: top
• significance: high
• originality: high
• clarity: top
• formatting: excellent
• grammar: perfect