https://doi.org/10.1140/epjp/s13360-024-05586-1
Regular Article
Complementarity between quantum entanglement and geometric and dynamical appearances in N spin-1/2 system under all-range Ising model
1
LPHE-Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco
2
Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco
3
Centre of Physics and Mathematics, CPM, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco
4
Department of Physics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco
Received:
16
July
2024
Accepted:
23
August
2024
Published online:
30
August
2024
With the growth of geometric science, including the methods of exploring the world of information by means of modern geometry, there has always been a mysterious and fascinating ambiguous link between geometric, topological and dynamical characteristics and quantum entanglement. Since geometry studies the interrelations between elements such as distance and curvature, it provides the information sciences with powerful structures that yield practically useful and understandable descriptions of integrable quantum systems. We explore here these structures in a physical system of N interaction spin-1/2 under all-range Ising model. By performing the system dynamics, we determine the Fubini–Study metric defining the relevant quantum state space. Applying Gaussian curvature within the scope of the Gauss–Bonnet theorem, we proved that the dynamics happens on a closed two-dimensional manifold having both a dumbbell-shaped structure and a spherical topology. The geometric and topological phases appearing during the system evolution processes are sufficiently discussed. Subsequently, we resolve the quantum brachistochrone problem by achieving the time-optimal evolution. By restricting the whole system to a two-spin-1/2 system, we investigate the relevant entanglement from two viewpoints: The first is of geometric nature and explores how the entanglement level affects derived geometric structures such as the Fubini–Study metric, the Gaussian curvature and the geometric phase; and the second is of dynamic nature and addresses the entanglement effect on the evolution speed and the related Fubini–Study distance. Further, depending on the degree of entanglement, we resolve the quantum brachistochrone problem.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
