Degrees and signatures of broken PT-symmetry in (non-uniform) lattices

TL;DR

This paper studies the robustness and signatures of broken PT-symmetry in non-uniform lattices with position-dependent hopping and symmetric impurities, revealing stronger symmetry phases and novel wavepacket dynamics.

Contribution

It demonstrates that PT-symmetric phases are more robust in non-uniform lattices and uncovers new phenomena in wavepacket evolution related to symmetry breaking.

Findings

PT-symmetric phase is stronger than in constant-hopping lattices

Wavepacket evolution differs notably between even and odd lattice sizes

Proximity of impurities influences symmetry-breaking signatures

Abstract

We investigate the robustness of parity- and time-reversal ($\mP\mT$) symmetric phase in an $N$-site lattice with position-dependent, parity-symmetric hopping function and a pair of imaginary, $\mP\mT$-symmetric impurities. We find that the "fragile" $\mP\mT$-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 $\mP\mT$-symmetry and their signatures in single-particle wavepacket evolution. We predict that when the $\mP\mT$-symmetric impurities are closest to each other, the time evolution of a wavepacket in an even-$N$ lattice is remarkably different from that in an odd-$N$ lattice. Our results suggest that $\mP\mT$-symmetry breaking in such lattices is accompanied by rich, hitherto unanticipated, phenomena.