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

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

2010-12-20

arxiv.org/abs/1012.4475v2

Phys. Rev. A 83, 050101(R) (2011)

Physics

Quantum Physics

10 pages, 3 figures; significant text and references revision

Scientific paper

10.1103/PhysRevA.83.050101

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.

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