Operator Space Transport and the Emergence of Boundary Time Crystals

Quantum Physics [Submitted on 15 Apr 2026] Operator Space Transport and the Emergence of Boundary Time Crystals Dominik Nemeth, Ahsan Nazir, Robert-Jan Slager, Alessandro Principi Boundary time crystals (BTCs) are prominent examples of continuous time crystals in collective spin systems governed by Lindbladian evolution. To date, their analysis has mostly relied on semiclassical and numerical approaches. Here, we develop a fully quantum-compatible framework to classify collective spin dynamics and show that BTC behavior emerges from the absence of non-trivial weak symmetries of the Liouvillian. To this end, we introduce an irreducible tensor representation of operator space, in which the Lindbladian dynamics maps onto a non-Hermitian hopping problem. Within this picture, the dynamics corresponds to the transport of operator weight across tensor sectors. This mapping allows an identification of distinct dynamical regimes, including collective precession, pure relaxation, and the BTC phase, within a single unified framework. We show that BTCs arise from non-reciprocal transport in operator space, which delocalizes Liouvillian eigenmodes across multiple tensor sectors. This non-reciprocal transport provides a microscopic mechanism for the insensitivity to initial conditions of BTC oscillations. More broadly, our results establish operator space transport as a perspective for understanding dissipative many-body dynamics and highlights connections to non-Hermitian phenomena. Comments: 16 pages, 6 figures Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2604.14291 [quant-ph]   (or arXiv:2604.14291v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.14291 Focus to learn more Submission history From: Dominik Nemeth [view email] [v1] Wed, 15 Apr 2026 18:00:04 UTC (409 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?)