The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart

TL;DR

This paper investigates a PT-symmetric tight-binding chain with position-dependent hopping, demonstrating its always stable PT phase, tunable energy spectrum, and predominantly extended eigenstates, with potential applications in waveguide systems.

Contribution

The study introduces a PT-symmetric chain with variable hopping that remains in the PT phase under general conditions, unlike constant-hopping models.

Findings

The model is always in the PT-symmetric phase.

Energy spectrum and density of states are highly tunable.

Eigenstates are mostly extended despite lack of translational symmetry.

Abstract

We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics which may be explored in coupled waveguides.