Abstract
In the Hermitian regime, uncorrelated disorder potential in one-dimensional lattice induces Anderson localization, whereas quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. In this study, we investigate the non-Hermitian regime. We analytically and numerically study Anderson localization in a one-dimensional lattice with the non-Hermitian complex disorder and quasiperiodic potential. We present a non-Hermitian Su-Schrieffer-Heeger (SSH) chain and demonstrate that the Hermitian counterpart with full real spectrum is a standard Anderson chain, which indicates that a nonzero imaginary disorder on-site potential can induce standard Anderson localization. We further demonstrate that the non-Hermitian Aubry-André -Harper (AAH) model exhibits a transition in parameter space, which separates the localization and delocalization phases and is determined by the self-duality of the model. This indicates that a pure imaginary quasiperiodic potential plays the same role as a real quasiperiodic potential in the transition point between localization and delocalization. Notably, a system with complex quasiperiodic potential exhibits an interference-like pattern on the transition points, which arises from the interplay between the real and imaginary components.
Highlights
The localization phase in quantum systems, which is originally rooted in condensed matter[1], has recently attracted a lot of theoretical and experimental interest in a variety of fields, including light waves in optical random media[2,3,4,5], matter waves in optical potential[6,7,8,9], sound waves in elastic media[10], and quantum chaotic systems[11], since the localization of quantum particles could prevent the transport necessary for equilibration in isolated systems
We present a non-Hermitian SSH chain to demonstrate that a nonzero imaginary disorder on-site potential can induce the standard Anderson localization
A system with complex quasiperiodic potential exhibits interference-like pattern on the transition point, i.e., the phase difference between real and imaginary quasiperiodic potential determines the boundary of transition
Summary
The localization phase in quantum systems, which is originally rooted in condensed matter[1], has recently attracted a lot of theoretical and experimental interest in a variety of fields, including light waves in optical random media[2,3,4,5], matter waves in optical potential[6,7,8,9], sound waves in elastic media[10], and quantum chaotic systems[11], since the localization of quantum particles could prevent the transport necessary for equilibration in isolated systems. Since the quasiperiodic potential does possess an intrinsic phase, the phase difference of real and imaginary quasiperiodic potential may influence the Anderson localization transition This is the main purpose of the present work. We show that the non-Hermitian Aubry-Andre (AA) model exhibits a transition in parameter space, which separates the localization and delocalization phases and is determined by the self-duality of the model It indicates that a pure imaginary quasiperiodic potential takes the same role as a real quasiperiodic potential in the transition point between localization and delocalization. II, we present a non-Hermitian SSH chain with disorder staggered balanced gain and loss We map this model to an equivalent Hermitian one and show the existence of Anderson localization.
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