Quantum geometric bounds at finite temperature for one-dimensional chiral systems

[2608.27944] Quantum geometric bounds at finite temperature for one-dimensional chiral systems Skip to main content Search Submit Donate Log in Condensed Matter > Mesoscale and Nanoscale Physics arXiv:2608.27944 (cond-mat) [Submitted on 28 Aug 2026] Title: Quantum geometric bounds at finite temperature for one-dimensional chiral systems Authors: Peng He , Hai-Tao Ding , Yu-Guo Liu View PDF HTML (experimental) Abstract: The geometry and topology of quantum states are intimately related at zero temperature through exact bounds that constrain geometric quantities from below by topological invariants. At finite-temperature, however, the analogous relations remain unclear. Here we establish rigorous geometric lower bounds for one-dimensional (1D) chiral-symmetric systems at finite temperature within the Uhlmann's framework for mixed states. We show that the Bures length is bounded by a continuous geometric phase angle. We further derive a temperature-dependent bound that interpolates between the zero-temperature limit and a trivial high-temperature regime. Our results are verified analytically and numerically using the Su-Schrieffer-Heeger (SSH) model and the spinless Kitaev chain model. Finally, we discuss potential ways to detect the geometry of the density matrix in quantum circuits, with the quantum imaginary time evolution (QITE) method. Comments: 9 pages, 3 figures Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ; Quantum Physics (quant-ph) Cite as: arXiv:2608.27944 [cond-mat.mes-hall] (or arXiv:2608.27944v1 [cond-mat.mes-hall] for this version) https://doi.org/10.48550/arXiv.2608.27944 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Peng He [ view email ] [v1] Fri, 28 Aug 2026 05:35:32 UTC (185 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mes-hall < prev | next > new | recent | 2026-08 Change to browse by: cond-mat quant-ph References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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