Boundary-sensitive non-Hermiticity of Floquet Hamiltonian: spectral transition and scale-free localization

Quantum Physics [Submitted on 24 Mar 2026] Boundary-sensitive non-Hermiticity of Floquet Hamiltonian: spectral transition and scale-free localization Bo Li, He-Ran Wang, Fei Song We report a novel mechanism of boundary-sensitive PT symmetry breaking in one-dimensional Floquet systems. By designing a time-periodic driving protocol, we realize a Floquet Hamiltonian that is Hermitian under periodic boundary conditions yet acquires non-Hermitian boundary terms under open boundary conditions due to the non-commutativity of driving Hamiltonians. We establish that a PT symmetry breaking transition occurs when the quasienergy bandwidth expands to cover the entire frequency Brillouin zone. This condition highlights a crucial difference from static non-Hermitian systems, where such transitions typically require band touching. Furthermore, we demonstrate that in the PT-broken phase, the eigenstates exhibit scale-free localization, a phenomenon arising from the specific system-size scaling of non-Hermitian terms. Finally, we provide a general framework for constructing multi-band models that exhibit this boundary-induced phase transition. Comments: 7 pages + 5 figures Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Optics (physics.optics) Cite as: arXiv:2603.22746 [quant-ph]   (or arXiv:2603.22746v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22746 Focus to learn more Submission history From: He-Ran Wang [view email] [v1] Tue, 24 Mar 2026 03:18:11 UTC (2,525 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.quant-gas physics physics.optics 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?)