Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
arXiv:2208.08733 · doi:10.1103/PhysRevB.106.144208
Abstract
The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the PT-symmetry.
9 pages, 10 figures
References in corpus (11)
- Topological phase transition in non-Hermitian quasicrystals
- Observation of Topological Phase Transitions in Photonic Quasicrystals
- Anderson localization in Bose-Einstein condensates
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Localization and adiabatic pumping in a generalized Aubry-André-Harper model
- Phase transitions in a non-Hermitian Aubry-André-Harper model
- Localization and topological transitions in non-Hermitian quasiperiodic lattices
- Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
- Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
- Fate of topological states in incommensurate generalized Aubry-André models
- Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics