Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions
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Quantum Physics arXiv:2605.06849 (quant-ph) [Submitted on 7 May 2026] Title:Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions Authors:Jakub Novotný, Jan Střeleček, Pavel Stránský, Pavel Cejnar View a PDF of the paper titled Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions, by Jakub Novotn\'y and 3 other authors View PDF HTML (experimental) Abstract:Motivated by the advance of dynamical quantum phase transitions (DQPTs), we analyze the zeros of the complex-time survival (Loschmidt) amplitude in finite quantum systems and develop a general framework for their approximation based on the stability of zeros of holomorphic functions. We show that the large-scale properties of the distribution of zeros are governed by the envelope of the energy distribution of the initial state and can be constructed from chains of periodic zeros associated with its dominant contributions. In this picture, zeros reach the real-time axis when two or more eigenstates become equally populated at the maximum of the envelope, providing a finite-size precursor of DQPTs. We apply the method to quenched ground states in the Ising model with tunable interaction range and demonstrate close agreement between the approximate and exact distributions of zeros. We prove that the approximate construction becomes exact for BCS ground-state quenches in two-band models. To describe short-time dynamics, we introduce a minimal Gaussian model with a nearly equidistant spectrum. Slow dephasing continuously deforms the initial zero pattern into the asymptotic two-level structure, explaining anomalous DQPTs as a delayed approach of zeros to the real-time axis. Our results identify the energy envelope as the key ingredient shaping dynamical critical behavior and provide a universal interpretation of the whole zero distribution of the complex-time survival amplitude. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.06849 [quant-ph] (or arXiv:2605.06849v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.06849 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jakub Novotný [view email] [v1] Thu, 7 May 2026 18:51:28 UTC (5,163 KB) Full-text links: Access Paper: View a PDF of the paper titled Tracing complex zeros of the quantum survival amplitude: How the energy distribution controls dynamical phase transitions, by Jakub Novotn\'y and 3 other authorsView PDFHTML (experimental)TeX Source 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?)