# Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane

### Submission summary

 As Contributors: Sriram Ganeshan Arxiv Link: https://arxiv.org/abs/1912.10805v3 (pdf) Date accepted: 2020-08-05 Date submitted: 2020-07-23 03:10 Submitted by: Ganeshan, Sriram Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approach: Theoretical

### Abstract

We study quantum dynamics on noncommutative spaces of negative curvature, focusing on the hyperbolic plane with spatial noncommutativity in the presence of a constant magnetic field. We show that the synergy of noncommutativity and the magnetic field tames the exponential divergence of operator growth caused by the negative curvature of the hyperbolic space. Their combined effect results in a first-order transition at a critical value of the magnetic field in which strong quantum effects subdue the exponential divergence for {\it all} energies, in stark contrast to the commutative case, where for high enough energies operator growth always diverge exponentially. This transition manifests in the entanglement entropy between the left' and right' Hilbert spaces of spatial degrees of freedom. In particular, the entanglement entropy in the lowest Landau level vanishes beyond the critical point. We further present a non-linear solvable bosonic model that realizes the underlying algebraic structure of the noncommutative hyperbolic plane with a magnetic field.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### Submission & Refereeing History

Resubmission 1912.10805v3 on 23 July 2020
Submission 1912.10805v2 on 30 December 2019

## Reports on this Submission

### Report

The Authors have addressed my points and comments provided in the earlier report, and at this point I have no further comments to add.

Given this, I would recommend this updated manuscript to be published accordingly, since it easily meets the criteria for publication in this journal.

• validity: good
• significance: ok
• originality: good
• clarity: good
• formatting: reasonable
• grammar: reasonable