Quench dynamics in nonreciprocal Aubry-André-Harper model
Abstract
The critical phase of a non-Hermitian quasicrystal can support stronger transport than its surrounding delocalized phase. We demonstrate this anomalous behavior in the one-dimensional nonreciprocal Aubry-André-Harper model through a combined study of dynamical quantum phase transitions (DQPTs) and wavepacket diffusion. Using a parity-sorted energy-spectrum classification that directly encodes the generalized 𝒫𝒯 symmetry, we find that DQPTs in this system are energy-resolved, in contrast to the energy-independent DQPTs of Hermitian quasicrystals. The energy-resolved features are most pronounced when the initial and final Hamiltonians belong to different phases (localized or extended), and they are tied to the even-odd index structure of the spectrum, which we exploit to organize the quench-dynamical landscape. For wavepacket dynamics after a single-site quench, the diffusion exponent β, extracted from the long-time power-law scaling of the root-mean-square displacement σ(τ), partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic (β=1), the critical phase is normally diffusive (β=0.5), and the localized phase yields β→ 0. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous β=1 at criticality to the self-similar multifractal structure of the critical eigenstates, whose nodal positions are organized by the golden ratio. A finite-size scaling ansatz built on the wave-front propagation yields σ(τ)∝τ. The parity-resolved DQPTs and the β-phase diagram establish two complementary dynamical diagnostics of nonreciprocal quasicrystals, in which nonreciprocity promotes transport at the critical point and suppresses it in the delocalized phase.
Related
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BibTeX
@misc{pei2026quench,
title = {{Quench dynamics in nonreciprocal Aubry-André-Harper model}},
author = {Zhiyu Pei and Yongxu Fu and Gao Xianlong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10342},
eprint = {2609.10342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10342},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quench dynamics in nonreciprocal Aubry-André-Harper model
AU - Zhiyu Pei
AU - Yongxu Fu
AU - Gao Xianlong
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10342
UR - https://arxiv.org/abs/2609.10342
AB - The critical phase of a non-Hermitian quasicrystal can support stronger transport than its surrounding delocalized phase. We demonstrate this anomalous behavior in the one-dimensional nonreciprocal Aubry-André-Harper model through a combined study of dynamical quantum phase transitions (DQPTs) and wavepacket diffusion. Using a parity-sorted energy-spectrum classification that directly encodes the generalized 𝒫𝒯 symmetry, we find that DQPTs in this system are energy-resolved, in contrast to the energy-independent DQPTs of Hermitian quasicrystals. The energy-resolved features are most pronounced when the initial and final Hamiltonians belong to different phases (localized or extended), and they are tied to the even-odd index structure of the spectrum, which we exploit to organize the quench-dynamical landscape. For wavepacket dynamics after a single-site quench, the diffusion exponent β, extracted from the long-time power-law scaling of the root-mean-square displacement σ(τ), partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic (β=1), the critical phase is normally diffusive (β=0.5), and the localized phase yields β→ 0. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous β=1 at criticality to the self-similar multifractal structure of the critical eigenstates, whose nodal positions are organized by the golden ratio. A finite-size scaling ansatz built on the wave-front propagation yields σ(τ)∝τ. The parity-resolved DQPTs and the β-phase diagram establish two complementary dynamical diagnostics of nonreciprocal quasicrystals, in which nonreciprocity promotes transport at the critical point and suppresses it in the delocalized phase.
ER -