Origin of maximal symmetry breaking in even PT-symmetric lattices

By investigating a parity and time-reversal (PT) symmetric, $N$-site lattice with impurities $\pm i\gamma$ and hopping amplitudes $t_0(t_b)$ for regions outside (between) the impurity locations, we probe the origin of maximal PT-symmetry breaking that occurs when the impurities are nearest neighbors. Through a simple and exact derivation, we prove that the critical impurity strength is equal to the hopping amplitude between the impurities, ${\gamma }_c=t_b$, and the simultaneous emergence of $N$ complex eigenvalues is a robust feature of any PT-symmetric hopping profile. Our results show that the threshold strength ${\gamma }_c$ can be widely tuned by a small change in the global profile of the lattice, and thus have experimental implications.