Convective and absolute PT-symmetry breaking in tight-binding lattices

We investigate the onset of parity-time (PT) symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss-gain regions in the presence of an advective term. Similarly to the instability properties of hydrodynamic open flows, it is shown that PT symmetry breaking can be either absolute or convective. In the former case, an initially localized wave packet shows a secular growth with time at any given spatial position, whereas in the latter case the growth is observed in a reference frame moving at some drift velocity while decay occurs at any fixed spatial position. In the convective unstable regime, PT symmetry is restored when the spatial region of gain or loss in the lattice is limited (rather than extended). We consider specifically a non-Hermitian extension of the Rice-Mele tight-binding lattice model, and show the existence of a transition from absolute to convective symmetry breaking when the advective term is large enough. An extension of the analysis to ac-dc driven lattices is also presented, and an optical implementation of the non-Hermitian Rice-Mele model is suggested, which is based on light transport in an array of evanescently coupled optical waveguides with a periodically bent axis and alternating regions of optical gain and loss.