Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane
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 g...
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| Format: | Article |
| Language: | English |
| Published: |
SciPost
2020-08-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.3.1.003 |
| _version_ | 1818606023223541760 |
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| author | Sriram Ganeshan, Alexios P. Polychronakos |
| author_facet | Sriram Ganeshan, Alexios P. Polychronakos |
| author_sort | Sriram Ganeshan, Alexios P. Polychronakos |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T14:04:15Z |
| format | Article |
| id | doaj.art-f8dda9845e684f4daff067cf603fcd64 |
| institution | Directory Open Access Journal |
| issn | 2666-9366 |
| language | English |
| last_indexed | 2024-12-16T14:04:15Z |
| publishDate | 2020-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj.art-f8dda9845e684f4daff067cf603fcd642022-12-21T22:28:58ZengSciPostSciPost Physics Core2666-93662020-08-013100310.21468/SciPostPhysCore.3.1.003Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic planeSriram Ganeshan, Alexios P. PolychronakosWe 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.https://scipost.org/SciPostPhysCore.3.1.003 |
| spellingShingle | Sriram Ganeshan, Alexios P. Polychronakos Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane SciPost Physics Core |
| title | Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| title_full | Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| title_fullStr | Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| title_full_unstemmed | Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| title_short | Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| title_sort | lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane |
| url | https://scipost.org/SciPostPhysCore.3.1.003 |
| work_keys_str_mv | AT sriramganeshanalexiosppolychronakos lyapunovexponentsandentanglemententropytransitiononthenoncommutativehyperbolicplane |