Localization transition in incommensurate non-Hermitian systems

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Mathematical physics

Background:

• One-dimensional lattice models are fundamental in condensed matter physics.
• Complex potentials introduce unique quantum phenomena.
• Localization transitions alter the behavior of quantum states.

Purpose of the Study:

• To investigate the localization transition in a specific class of 1D lattice models.
• To analyze the role of incommensurate complex potentials in quantum localization.
• To characterize the behavior of the complex eigenspectrum during the transition.

Main Methods:

• Analysis of a one-dimensional lattice model with a specific complex potential: V(theta)=2[lambda(r) cos(theta)+i(lambda)(i) sin(theta)].
• Examination of the complex eigenspectrum to identify signatures of localization.
• Study of the measure of states with real eigenenergies in different phases.

Main Results:

• A localization transition occurs at the critical point |lambda(r)| + |lambda(i)| = 1.
• The transition is characterized by the measure of real eigenenergy states vanishing in the localized phase.
• Extended states exhibit real spectra when |lambda(r)| >= |lambda(i)|.
• The imaginary part of the spectrum is boundary-condition dependent only near the localization onset.

Conclusions:

• The studied 1D lattice models exhibit a clear localization transition driven by complex potentials.
• The complex eigenspectrum serves as a robust indicator of extended versus localized states.
• The findings offer insights into quantum transport and Anderson localization in complex systems.