Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity

Quantum Physics [Submitted on 14 Apr 2026] Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity M. Süzen A time-integrated measure of complexity is proposed for diagnosing the degree of quantum ergodicity. The scrambling dynamics of maximally entangled states within the ensemble of unitary evolutions are quantified by applying numerical bootstrapped realizations of an ensemble of Hamiltonians, probing different unitary paths. Using Rosenzweig-Porter ensembles, we show that the integrated spread complexity provides a fine-grained resolution across different ergodic regimes. This approach offers a robust method for diagnosing quantum chaos from early to late times. Comments: 6 pages, 4 figures, initial public release, PACS: this http URL, this http URL, 81Qxx, 02.60.C Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) MSC classes: 81Qxx, 37M05, 15A60 ACM classes: G.2.2 Cite as: arXiv:2604.14224 [quant-ph]   (or arXiv:2604.14224v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.14224 Focus to learn more Submission history From: Mehmet A. Süzen PhD [view email] [v1] Tue, 14 Apr 2026 13:16:20 UTC (125 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)