Impurity-induced loss bursts from anomalous scale-free localization in a non-Hermitian dissipative lattice

@misc{liu2026impurityinduced,
  title = {{Impurity-induced loss bursts from anomalous scale-free localization in a non-Hermitian dissipative lattice}},
  author = {Hui Liu and Zhihao Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.21034},
  eprint = {2605.21034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.21034},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Impurity-induced loss bursts from anomalous scale-free localization in a non-Hermitian dissipative lattice
AU  - Hui Liu
AU  - Zhihao Xu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.21034
UR  - https://arxiv.org/abs/2605.21034
AB  - We identify anomalous scale-free localization and associated impurity-induced loss bursts in a non-Hermitian dissipative cross-stitch lattice. By a local basis rotation, the model is mapped onto an effective non-Hermitian Su-Schrieffer-Heeger lattice, where local impurities act as tunable effective boundaries. For the parameter choice considered here, the impurity-free periodic-boundary-condition point is reached at η=1. Tuning η away from this point drives the system through generalized-boundary-condition regimes toward two effective open-boundary-condition-like limits at η→0 and η→∞. For finite η∉{0,1}, the loop-sector spectra remain separated from the real-energy axis, while the corresponding eigenstates exhibit scale-free localization pinned by the impurity. Unlike conventional impurity-induced scale-free localization, the Lyapunov exponent depends explicitly on the eigenenergy, making the localization strength eigenstate dependent. We further show that this anomalous eigenmode structure produces an impurity-induced loss burst: The long-time integrated dissipation probability develops a pronounced local enhancement relative to the surrounding background near an impurity-generated effective boundary, even when the initial wave packet is prepared far away. In the single-impurity case, the burst region consists of the impurity site and its adjacent effective-boundary site, and the effect occurs without imaginary-gap closing. For multiple impurities, local burst regions emerge around all impurities, while the dominant burst boundary is selected by the initial wave-packet position and the nonreciprocal drift direction. These results connect anomalous scale-free localization with controllable dissipation dynamics in non-Hermitian lattices.
ER  -