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

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.

10 pages, 3 figures; significant text and references revision

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• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Tunable waveguide lattices with non-uniform parity-symmetric tunneling
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Exceptional points in oligomer chains
• Unitary Scattering Protected by Pseudo-Hermiticity
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Robust incoherent perfect absorption
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring
• Exceptional spectrum and dynamic magnetization
• Resilience of $\mathcal{P}\mathcal{T}$ symmetry against stochasticity in a gain-loss balanced oscillator