R\'enyi Phase Transitions and Analytic Continuation to the von Neumann Entropy

Quantum Physics arXiv:2609.30386 (quant-ph) [Submitted on 24 Sep 2026] Title:Rényi Phase Transitions and Analytic Continuation to the von Neumann Entropy Authors:Ayush Raj, Akash Vijay, Hong-Chen Jiang, Laimei Nie View a PDF of the paper titled R\'enyi Phase Transitions and Analytic Continuation to the von Neumann Entropy, by Ayush Raj and 3 other authors View PDF HTML (experimental) Abstract:Extracting operationally meaningful quantities such as von Neumann entropy and mutual information is central to characterizing many-body quantum systems, yet experiments and numerics often provide direct access only to integer Rényi entropies. Whereas conventional extrapolation relies on a prescribed fitting ansatz, in PRL 137, 100202 we introduced an alternative approach based on stabilized analytic continuation (SAC), which avoids such an ansatz and is inherently robust to noise. Here, we further develop this framework in the noiseless setting and benchmark its performance across several nontrivial many-body problems. We first show that, besides the intrinsic ambiguity of reconstructing the von Neumann entropy from finitely many Rényi samples, analytic continuation can also fail because of genuine nonanalyticities in the Rényi function arising from zeros of $\text{Tr}\rho^z$. We derive universal zero-free domains for $\text{Tr}\rho^z$ and systematically sharpen these bounds using additional spectral information about $\rho$. We then benchmark the performance of SAC in three settings: ($i$) extracting topological entanglement entropy from DMRG Rényi data for the toric code and Kagome Heisenberg models; ($ii$) reconstructing the mutual information between disjoint intervals in a $(1+1)d$ compact-boson CFT; and ($iii$) recovering finite-time ballistic growth of the von Neumann entropy from integer Rényi entropies that cross over toward subballistic growth in diffusive quantum dynamics. In the latter setting, analytic continuation is expected to fail in the long time limit. We illustrate this mechanism with a physically motivated two-sector model, where the asymptotic separation between von Neumann and higher-Rényi growth is accompanied by a zero of $\text{Tr}\rho^z$ pinching the real axis at $z=1$, thereby producing a first-order Rényi phase transition. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2609.30386 [quant-ph] (or arXiv:2609.30386v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.30386 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ayush Raj [view email] [v1] Thu, 24 Sep 2026 18:00:43 UTC (1,357 KB) Full-text links: Access Paper: View a PDF of the paper titled R\'enyi Phase Transitions and Analytic Continuation to the von Neumann Entropy, by Ayush Raj and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.stat-mech 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?)