The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value Vc of the quasiperiodic potential amplitude V. In terms of dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent δ of wave packet spreading, with δ=1 in the delocalized phase VVc (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed v(V) of excitation transport in the lattice, which is a continuous function of potential amplitude V and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-André-Harper model, in which hopping along the lattice is asymmetric, and show that the dynamical localization-delocalization transition is discontinuous not only in the diffusion exponent δ, but also in the speed v of ballistic transport. This means that, even very close to the spectral phase transition point, rather counter-intuitively ballistic transport with a finite speed is allowed in the lattice. Also, we show that the ballistic velocity can increase as V is increased above zero, i.e. surprisingly disorder in the lattice can result in an enhancement of transport.

The author acknowledges the Spanish State Research Agency through the Severo Ochoa and Mara de MaeztuProgram for Centers and Units of Excellence in R&D (Grant No. MDM-2017-0711).

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