Measure-zero delocalization in the complex plane: exact mobility arcs in a non-Hermitian off-diagonal quasiperiodic lattice
Abstract
We investigate Anderson localization in a one-dimensional lattice with non-Hermitian off-diagonal quasiperiodic disorder, extending a recently studied Hermitian mosaic model to the non-Hermitian regime. Using Avila's global theory, we derive the exact Lyapunov exponent and the complete phase diagram in the complex energy plane. This work contains two central findings. First, we discover mobility arcs---open curved segments in the complex plane---as a new class of mobility edges and the generic form of open mobility edges, which coexist with closed mobility rings in a complementary parameter regime. These arcs share the same localization physics as the previously reported mobility lines: eigenstates are delocalized if and only if their energies lie exactly on these sets; any deviation yields localized states. This constitutes a striking measure-zero delocalization phenomenon: delocalized states occupy only zero-measure sets (arcs or lines) in the complex plane, in sharp contrast to the mobility rings, which enclose a finite-area region of delocalized states. Second, we reveal that mobility rings, arcs, and lines all share a common mathematical origin in the generalized Joukowski transformation P(E) = 1/2(u − w2/u), rooted in the algebraic structure of the underlying polynomial: the preimage of the boundary of an elliptical region under the polynomial map P(E) gives the rings, while the branch cut inside this ellipse gives rise to the mobility arcs and lines in the complementary parameter regime.
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BibTeX
@misc{zhong2026measurezero,
title = {{Measure-zero delocalization in the complex plane: exact mobility arcs in a non-Hermitian off-diagonal quasiperiodic lattice}},
author = {Fu-Xi Zhong and Yi-Cai Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25877},
eprint = {2609.25877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25877},
}
RIS
TY - UNPB
TI - Measure-zero delocalization in the complex plane: exact mobility arcs in a non-Hermitian off-diagonal quasiperiodic lattice
AU - Fu-Xi Zhong
AU - Yi-Cai Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25877
UR - https://arxiv.org/abs/2609.25877
AB - We investigate Anderson localization in a one-dimensional lattice with non-Hermitian off-diagonal quasiperiodic disorder, extending a recently studied Hermitian mosaic model to the non-Hermitian regime. Using Avila's global theory, we derive the exact Lyapunov exponent and the complete phase diagram in the complex energy plane. This work contains two central findings. First, we discover mobility arcs---open curved segments in the complex plane---as a new class of mobility edges and the generic form of open mobility edges, which coexist with closed mobility rings in a complementary parameter regime. These arcs share the same localization physics as the previously reported mobility lines: eigenstates are delocalized if and only if their energies lie exactly on these sets; any deviation yields localized states. This constitutes a striking measure-zero delocalization phenomenon: delocalized states occupy only zero-measure sets (arcs or lines) in the complex plane, in sharp contrast to the mobility rings, which enclose a finite-area region of delocalized states. Second, we reveal that mobility rings, arcs, and lines all share a common mathematical origin in the generalized Joukowski transformation P(E) = 1/2(u − w^2/u), rooted in the algebraic structure of the underlying polynomial: the preimage of the boundary of an elliptical region under the polynomial map P(E) gives the rings, while the branch cut inside this ellipse gives rise to the mobility arcs and lines in the complementary parameter regime.
ER -