In the familiar Hermitian Aubry-André-Harper (AAH) model, transport is fastest in the extended (delocalized) phase and absent in the localized phase, with the critical point sitting in between as ordinary diffusion. A preprint posted to arXiv — not yet peer-reviewed — reports that introducing nonreciprocal hopping (unequal forward and backward amplitudes) inverts this ordering: the critical phase becomes ballistic (diffusion exponent β = 1) while the extended phase is demoted to normal diffusion (β = 0.5).
The authors combine two complementary diagnostics. First, they study dynamical quantum phase transitions (DQPTs) following a sudden quench, finding that — unlike Hermitian quasicrystals, where DQPTs are energy-independent — the non-Hermitian system exhibits energy-resolved DQPTs tied to an even-odd parity structure of the spectrum that encodes the system's generalized PT symmetry. Second, they track wavepacket spreading after a single-site quench, extracting power-law exponents that partition the full phase diagram into four dynamically distinct regimes. The anomalous ballistic transport at criticality is attributed to the self-similar, golden-ratio-organized nodal structure of the multifractal critical eigenstates, supported by a finite-size scaling ansatz for the wave-front propagation.
The work is a theoretical study of a one-dimensional lattice model and has not yet undergone peer review. If the results hold up, the parity-resolved DQPT signature and the β-phase diagram would offer two independent dynamical fingerprints for diagnosing non-Hermitian quasicrystalline phases — and suggest that nonreciprocity can be a resource for enhancing transport precisely where Hermitian physics would predict it to be weakest.