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

TL;DR

This paper explores PT-symmetry breaking in a ring lattice with gain and loss impurities, revealing a universal chirality at the phase transition point and showing the robustness of the PT-symmetric phase.

Contribution

It demonstrates the robustness of the PT-symmetric phase in a ring lattice and uncovers universal chirality behavior at the symmetry-breaking threshold.

Findings

PT-symmetry phase is insensitive to impurity distance

Critical impurity strength is given by |t0 - tb|

Chirality reaches a universal maximum at the phase boundary

Abstract

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 $\pm i\gamma$, 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 $\gamma_{PT}=|t_0-t_b|$. 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 $\gamma$, and the chirality reaches a universal maximum value at the threshold, $\gamma=\gamma_{PT}$, 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.