Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem
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Quantum Physics arXiv:2512.11093 (quant-ph) [Submitted on 11 Dec 2025] Title:Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem Authors:Samuel M. Soares, Lucas Squillante, Henrique S. Lima, Constantino Tsallis, Mariano de Souza View a PDF of the paper titled Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem, by Samuel M. Soares and 4 other authors View PDF HTML (experimental) Abstract:We investigate the influence of the spin magnitude $S$ on the quantum Grüneisen parameter $\Gamma^{0\text{K}}_q$ right at critical points (CPs) for the 1D Ising model under a transverse magnetic field. Our findings are fourfold: $\textit{i)}$ for higher $S$, $\Gamma^{0\text{K}}_q$ is increased, but remains finite, reflecting the enhancement of the Hilbert space dimensionality; $\textit{ii)}$ the Schmidt decomposition theorem recovers the extensivity of the nonadditive $q$-entropy $S_q$ only for a $\textit{special}$ value of the entropic index $q$; $\textit{iii)}$ the universality class in the frame of $S_q$ depends only on the symmetry of the system; $\textit{iv)}$ we propose an experimental setup to explore finite size effects in connection with the Hilbert space occupation at CPs. Our findings unveil both universal and non-universal aspects of quantum criticality in terms of $\Gamma^{0\text{K}}_q$ and $S_q$. Comments: Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Statistical Mechanics (cond-mat.stat-mech); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:2512.11093 [quant-ph] (or arXiv:2512.11093v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.11093 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mariano de Souza Prof. Dr. [view email] [v1] Thu, 11 Dec 2025 20:09:23 UTC (2,491 KB) Full-text links: Access Paper: View a PDF of the paper titled Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem, by Samuel M. Soares and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.other cond-mat.stat-mech physics physics.data-an 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)