Origin of maximal symmetry breaking in evenPT-symmetric lattices

By investigating a parity- and time-reversal- (PT-) symmetric, N-site lattice with impurities ±iγ and hopping amplitudes t₀0.28em0ex(tb) for regions outside (between) the impurity locations, we probe the interimpurity-distance dependence of the critical impurity strength and 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, γc=tb, 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 γc can be widely tuned by a small change in the global profile of the lattice and thus have experimental implications.