Fig. 1: Intertwinement of the triple phase transition in the non-Hermitian Floquet AAH model.

By intertwining a one-dimensional quasicrystal (AAH model) with a non-Hermitian anisotropy (skin effect model) via a temporal driving (Floquet mechanism), one obtains the non-Hermitian Floquet AAH model that is discussed in this work. Although none of the models on the left show a phase transition, except for a localization transition in the AAH model, the combined model on the right shows a triple phase transition, that is, a localization phase transition and a topological phase transition are connected to spontaneous PT symmetry breaking (energy-conservation transition). All three transitions occur at the same critical point of a single parameter, which can be a purely Hermitian parameter (the coupling strength) or a purely non-Hermitian parameter (the anisotropy strength).