Isospectrality and Operator Complexity

Quantum Physics [Submitted on 3 Jun 2026] Isospectrality and Operator Complexity Pradip Kattel, Yicheng Tang, Natan Andrei We study a pair of exactly solvable, isospectral fermion chains, one strongly interacting and one quadratic, that nevertheless display remarkably different phase structures and operator dynamics. A nonlocal nonlinear unitary transformation maps one onto the other while preserving the entire many-body spectrum and converting local fermion operators into extended many-body strings. Thus, operators that evolve within a closed linear subspace in the quadratic model become interacting operators that generate increasingly higher-body terms and exhibit asymptotic Lanczos growth b_n\propto\sqrt n. Despite their identical spectra, the two models realize distinct phases and sharply different notions of operator complexity. Our results demonstrate that free many-body spectra and interacting operator dynamics are fundamentally compatible. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con); Mathematical Physics (math-ph) Cite as: arXiv:2606.05294 [quant-ph]   (or arXiv:2606.05294v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05294 Focus to learn more Submission history From: Pradip Kattel [view email] [v1] Wed, 3 Jun 2026 18:00:05 UTC (309 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el cond-mat.supr-con math math-ph math.MP 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?)