Degrees and signatures of broken PT symmetry in nonuniform lattices

We investigate the robustness of the parity-and time-reversal (PT) symmetric phase in an N-site lattice with a position-dependent, parity-symmetric hopping function and a pair of imaginary, PT-symmetric impurities. We find that the fragile PT-symmetric phase in these lattices is stronger than its counterpart in a lattice with constant hopping. With an open system in mind, we explore the degrees of broken PT symmetry and their signatures in single-particle wave-packet evolution. We predict that, when the PT-symmetric impurities are closest to each other, the time evolution of a wave packet in an even-N lattice is remarkably different from that in an odd-N lattice. Our results suggest that PT symmetry breaking in such lattices is accompanied by rich, hitherto unanticipated, phenomena.