Quench dynamics in nonreciprocal Aubry-Andr\'e-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 $\mathcal{PT}$ 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 $\beta$, extracted from the long-time power-law scaling of the root-mean-square displacement $\sigma(\tau)$, partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic ($\beta=1$), the critical phase is normally diffusive ($\beta=0.5$), and the localized phase yields $\beta\to 0$. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous $\beta=1$ 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 $\sigma(\tau)\propto\tau$. The parity-resolved DQPTs and the $\beta$-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.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2609.10342 [cond-mat.mes-hall]

(or arXiv:2609.10342v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2609.10342 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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