PT-symmetry breaking and universal chirality in a PT-symmetric ring

We investigate the properties of an $N$-site tight-binding lattice with periodic boundary condition (PBC) in the presence of a pair of gain and loss impurities $\pm iγ$, and two tunneling amplitudes $t_0,t_b$ that are constant along the two paths that connect them. We show that the parity and time-reversal ($\mP\mT$)-symmetric phase of the lattice with PBC is robust, insensitive to the distance between the impurities, and that the critical impurity strength for PT-symmetry breaking is given by $γ_{PT}=|t_0-t_b|$. We study the time-evolution of a typical wave packet, initially localized on a single site, across the PT-symmetric phase boundary. We find that it acquires chirality with increasing $γ$, and the chirality reaches a universal maximum value at the threshold, $γ=γ_{PT}$, irrespective of the initial location of the wave packet or the lattice parameters. Our results imply that PT-symmetry breaking on a lattice with PBC has consequences that have no counterpart in open chains.

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