- Accepted Paper
Scale-free localization in pseudo-Hermitian quantum walk
Phys. Rev. Lett. - Accepted 14 October, 2026
DOI: https://doi.org/10.1103/mqng-hgb1
Phys. Rev. Lett. - Accepted 14 October, 2026
DOI: https://doi.org/10.1103/mqng-hgb1
Scale-free localization is a distinctive phenomenon in non-Hermitian systems, where specific eigenstates, known as scale-free localized states (LSs), possess localization lengths that scale linearly with the system size. Here, we show that a single non-Hermitian defect in one-dimensional quantum walks (QWs) induces scale-free localization. Driven by non-Hermiticity, the QW system respects pseudo-Hermitian (PH) phase transition and the PH symmetry breaking is accompanied by the emergence of scale-free localization. As non-Hermiticity is further increased, the system undergoes a second phase transition, marked by the emergence of two pairs of bound states. Crucially, we identify the critical points of both transitions using localization properties. Furthermore, we extend our investigation to two-dimensional QWs, where a single non-Hermitian defect also induced scale-free localization, thereby demonstrating the universality of this phenomenon. Our work provides a valuable perspective for further exploring defect physics and a type of novel LSs in non-Hermitian quantum systems.
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