Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

Abstract

Non-Hermitian extensions of the Anderson and Aubry-André-Harper models are attracting a considerable interest as platforms to study localization phenomena, metal-insulator and topological phase transitions in disordered non-Hermitian systems. Most of available studies, however, resort to numerical results, while few analytical and rigorous results are available owing to the extraordinary complexity of the underlying problem. Here we consider a parity-time (PT ) symmetric extension of the Aubry-André-Harper model, undergoing a topological metal-insulator phase transition, and provide rigorous analytical results of energy spectrum, symmetry breaking phase transition and localization length. In particular, by extending to the non-Hermitian realm the Thouless ′ s result relating localization length and density of states, we derive an analytical form of the localization length in the insulating phase, showing that -like in the Hermitian Aubry-André-Harper modelthe localization length is independent of energy.

Phase transitions in a non-Hermitian Aubry-André-Harper model

“…The energy spectrum of this model can be determined in an exact form, as shown in Appendix B (see also [65]). The main results can be summarized as follows:…”

“…Recently, fresh and new perspectives on spectral localization, transport, and topological phase transitions have been disclosed in non-Hermitian lattices, where complex on-site potentials or asymmetric hopping are phenomenologically introduced to describe system interaction with the surrounding environment [29,. In particular, the interplay of aperiodic order and non-Hermiticity has been investigated in several recent works [62][63][64][65][66][67][68][69][70][71][72][73][74], revealing that the phase transition of eigenstates, from exponentially localized to extended (under periodic boundary conditions), can be often related to the change of topological (winding) numbers of the energy spectrum [55,64,72]. However, the dynamical behavior of the system near the phase transition, probed by the diffusion exponent or propagation speed of excitation, remains so far largely unexplored.…”

Helical resonant transport and purified amplification at an exceptional point

“…(A10) and (A11) (see Appendix A), we can see that the quasi-1D system support the perfect transmission and interfered transmission; while it can not be used to observe the purified amplification dynamic proposed in the 2D system. The non-Hermitian SSH model is a prototypical topological model, further study on the application of other PT -symmetric non-Hermitian topological system [64][65][66] and topological system with non-Hermitian skin effect [67,68] will be interesting. All these 1D and quasi-1D systems are ready to be realized in the experiments [69,70].…”

Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices

“…A seminal work dealing with disorder in non-Hermitian lattices is the Hatano-Nelson model [62,65,66], in which an asymmetric hopping caused by an imaginary gauge field results in a localization-delocalization transition and the existence of mobility edges [67]. Since this pioneering study, several non-Hermitian models with either random or incommensurate disorder have been investigated, in which non-Hermiticity is introduced by either asymmetric hopping amplitudes or complex on-site potentials [68][69][70][71][72][73][74][75][76][77][78][79]. In certain models, the topological nature of the localization transition and self-duality have been discussed [36,77,79].…”