Enhanced Multifractality Induced by Non-Hermitian Disorder in Quantum Percolation
Abstract
We investigate the interplay between geometric dilution and non-Hermitian disorder in the two-dimensional quantum site-percolation model. Non-Hermiticity is introduced through random imaginary on-site potentials, representing spatially uncorrelated gain and loss, while the hopping amplitudes remain reciprocal. By combining complex level-spacing statistics, participation entropy, and multifractal analysis, we characterize the localization properties of the eigenstates as functions of the disorder and the non-Hermiticity strength. Our finite-size scaling results show that non-Hermitian disorder shifts the quantum percolation threshold (pq) toward larger occupation probabilities. Consequently, the fully delocalized phase is progressively suppressed and disappears at sufficiently strong disorder. This suppression is not a simple consequence of adding on-site disorder of a given strength, but is specifically enhanced by its imaginary character, as an equally strong real (Hermitian) on-site potential produces a weaker shift of pq. Nevertheless, the intermediate region between the classical (pc) and quantum percolation thresholds presents a genuine multifractal critical phase, while the localization-length exponent ν remains the same, relative to its Hermitian value. Altogether, our results demonstrate that random gain and loss enhance the multifractal regime while preserving the universality class of the quantum percolation transition.
Related
- Duality Between Twist-Angle Disorder and Non-Hermitian Disorder
- Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions
- Hilbert space connectivity in non-Hermitian many-body systems: emergent scale-dependent amplification and constraint-induced skin localization
- Non-Hermitian Cooperation Induced Chern Insulator
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BibTeX
@misc{oliveira2026enhanced,
title = {{Enhanced Multifractality Induced by Non-Hermitian Disorder in Quantum Percolation}},
author = {W. S. Oliveira and Julian Faundez and Rodrigo Arouca and Welles Morgado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04625},
eprint = {2609.04625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04625},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Enhanced Multifractality Induced by Non-Hermitian Disorder in Quantum Percolation
AU - W. S. Oliveira
AU - Julian Faundez
AU - Rodrigo Arouca
AU - Welles Morgado
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04625
UR - https://arxiv.org/abs/2609.04625
AB - We investigate the interplay between geometric dilution and non-Hermitian disorder in the two-dimensional quantum site-percolation model. Non-Hermiticity is introduced through random imaginary on-site potentials, representing spatially uncorrelated gain and loss, while the hopping amplitudes remain reciprocal. By combining complex level-spacing statistics, participation entropy, and multifractal analysis, we characterize the localization properties of the eigenstates as functions of the disorder and the non-Hermiticity strength. Our finite-size scaling results show that non-Hermitian disorder shifts the quantum percolation threshold (p_q) toward larger occupation probabilities. Consequently, the fully delocalized phase is progressively suppressed and disappears at sufficiently strong disorder. This suppression is not a simple consequence of adding on-site disorder of a given strength, but is specifically enhanced by its imaginary character, as an equally strong real (Hermitian) on-site potential produces a weaker shift of p_q. Nevertheless, the intermediate region between the classical (p_c) and quantum percolation thresholds presents a genuine multifractal critical phase, while the localization-length exponent ν remains the same, relative to its Hermitian value. Altogether, our results demonstrate that random gain and loss enhance the multifractal regime while preserving the universality class of the quantum percolation transition.
ER -