Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement

Quantum Physics arXiv:2605.00241 (quant-ph) [Submitted on 30 Apr 2026] Title:Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement Authors:Jamal Elfakir View a PDF of the paper titled Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement, by Jamal Elfakir View PDF Abstract:This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of symplectic structures in describing mechanical states. The study highlights the formal analogy between classical phase space and the Hilbert space used in quantum mechanics. The second part is devoted to the geometric description of quantum states through the projective structure of Hilbert space. Emphasis is placed on the geometric interpretation of quantum evolution, particularly via the Fubini-Study metric, associated symplectic structures, and the geometric phase acquired during unitary evolutions. The final two parts are dedicated to the study of spin systems (both two-body and many-body) under different interaction models (XXZ Heisenberg and all-range Ising). Both the dynamical aspects (evolution speed, entanglement, and the quantum brachistochrone problem) and the geometric and topological structures of the corresponding quantum states are analyzed. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.00241 [quant-ph] (or arXiv:2605.00241v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.00241 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jamal Elfakir Dr. [view email] [v1] Thu, 30 Apr 2026 21:21:13 UTC (3,204 KB) Full-text links: Access Paper: View a PDF of the paper titled Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement, by Jamal ElfakirView PDF view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)