Spectral and dynamical characters of 1D incommensurate optical lattices with [formula omitted]-symmetry

Abstract

In this paper, we investigate the spectral and dynamical properties of a 1D incommensurate optical lattice, which displays a Parity-time (PT) symmetry described by the Non-Hermitian Aubry–André potential. We show through the spectral analysis of the eigenvalues and the associated eigenfunctions that, taking into account a non-Hermitian variant of the site energy modulated by a cosine form, leads the system to undergo a transition from the unbroken-PT phase to the broken-PT phase, which corresponds here to the delocalized-to-localized phase transition. Our findings also indicate that the critical point of transition can be selectively adjusted and consequently, the single-particle eigenstates taken in the metallic regime of the original Aubry–André model thus move from a conducting state to an insulating one upon an increase of the complex phase parameter. Furthermore, we also investigate the dynamical features of the system’s wave function according to different parameters.