Scale-free localization in pseudo-Hermitian quantum walk
Abstract
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 undergoes a 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 induces 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 LS in non-Hermitian quantum systems.
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BibTeX
@misc{zhang2026scalefree,
title = {{Scale-free localization in pseudo-Hermitian quantum walk}},
author = {Haiting Zhang and Lei Xiao and Cui-Xian Guo and Quan Lin and Peng Xue},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31067},
eprint = {2610.31067},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31067},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scale-free localization in pseudo-Hermitian quantum walk
AU - Haiting Zhang
AU - Lei Xiao
AU - Cui-Xian Guo
AU - Quan Lin
AU - Peng Xue
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31067
UR - https://arxiv.org/abs/2610.31067
AB - 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 undergoes a 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 induces 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 LS in non-Hermitian quantum systems.
ER -